{"id":"https://openalex.org/W2003288973","doi":"https://doi.org/10.1305/ndjfl/1091030855","title":"On Sequentially Compact Subspaces of without the Axiom of Choice","display_name":"On Sequentially Compact Subspaces of without the Axiom of Choice","publication_year":2003,"publication_date":"2003-07-01","ids":{"openalex":"https://openalex.org/W2003288973","doi":"https://doi.org/10.1305/ndjfl/1091030855","mag":"2003288973"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1091030855","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1091030855","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-44/issue-3/On-Sequentially-Compact-Subspaces-of--without-the-Axiom-of/10.1305/ndjfl/1091030855.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-44/issue-3/On-Sequentially-Compact-Subspaces-of--without-the-Axiom-of/10.1305/ndjfl/1091030855.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028285276","display_name":"Kyriakos Keremedis","orcid":"https://orcid.org/0000-0001-8453-3477"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]},{"id":"https://openalex.org/I98805295","display_name":"University of the Aegean","ror":"https://ror.org/03zsp3p94","country_code":"GR","type":"education","lineage":["https://openalex.org/I98805295"]}],"countries":["GR","US"],"is_corresponding":false,"raw_author_name":"Kyriakos Keremedis","raw_affiliation_strings":["Department of Statistics and Actuarial Science University of the Aegean Karlovassi Samos 83200 GREECE","University of Notre Dame Department of Mathematics","University of the Aegean Karlovassi Samos 83200 GREECE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Actuarial Science University of the Aegean Karlovassi Samos 83200 GREECE","institution_ids":[]},{"raw_affiliation_string":"University of Notre Dame Department of Mathematics","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"University of the Aegean Karlovassi Samos 83200 GREECE","institution_ids":["https://openalex.org/I98805295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000502133","display_name":"Eleftherios Tachtsis","orcid":"https://orcid.org/0000-0001-9114-3661"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]},{"id":"https://openalex.org/I98805295","display_name":"University of the Aegean","ror":"https://ror.org/03zsp3p94","country_code":"GR","type":"education","lineage":["https://openalex.org/I98805295"]}],"countries":["GR","US"],"is_corresponding":false,"raw_author_name":"Eleftherios Tachtsis","raw_affiliation_strings":["Department of Statistics and Actuarial Science University of the Aegean Karlovassi Samos 83200 GREECE","University of Notre Dame Department of Mathematics","University of the Aegean Karlovassi Samos 83200 GREECE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Actuarial Science University of the Aegean Karlovassi Samos 83200 GREECE","institution_ids":[]},{"raw_affiliation_string":"University of Notre Dame Department of Mathematics","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"University of the Aegean Karlovassi Samos 83200 GREECE","institution_ids":["https://openalex.org/I98805295"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8312,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.68533751,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"44","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.9814000129699707,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9711999893188477,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.7906269431114197},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7821840047836304},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7434720396995544},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6950536966323853},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.6834365725517273},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.6397097110748291},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.5730312466621399},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5565546751022339},{"id":"https://openalex.org/keywords/disjoint-union","display_name":"Disjoint union (topology)","score":0.5350445508956909},{"id":"https://openalex.org/keywords/tychonoff-space","display_name":"Tychonoff space","score":0.5207069516181946},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49583443999290466},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.49483293294906616},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.41919535398483276},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.411201149225235},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4099901616573334},{"id":"https://openalex.org/keywords/hausdorff-space","display_name":"Hausdorff space","score":0.3523467183113098},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.23272472620010376},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2033626139163971},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11445742845535278}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.7906269431114197},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7821840047836304},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7434720396995544},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6950536966323853},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.6834365725517273},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6397097110748291},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.5730312466621399},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5565546751022339},{"id":"https://openalex.org/C7655956","wikidata":"https://www.wikidata.org/wiki/Q5282259","display_name":"Disjoint union (topology)","level":2,"score":0.5350445508956909},{"id":"https://openalex.org/C87142424","wikidata":"https://www.wikidata.org/wiki/Q1191433","display_name":"Tychonoff space","level":3,"score":0.5207069516181946},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49583443999290466},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.49483293294906616},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.41919535398483276},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.411201149225235},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4099901616573334},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.3523467183113098},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.23272472620010376},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2033626139163971},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11445742845535278},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1091030855","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1091030855","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-44/issue-3/On-Sequentially-Compact-Subspaces-of--without-the-Axiom-of/10.1305/ndjfl/1091030855.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1091030855","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1091030855","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1305/ndjfl/1091030855","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1091030855","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-44/issue-3/On-Sequentially-Compact-Subspaces-of--without-the-Axiom-of/10.1305/ndjfl/1091030855.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2003288973.pdf"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W799338602","https://openalex.org/W1541012876","https://openalex.org/W1608084331","https://openalex.org/W1990682234","https://openalex.org/W2016396872","https://openalex.org/W2017523153","https://openalex.org/W2020053991","https://openalex.org/W2034914951","https://openalex.org/W2035802665","https://openalex.org/W2063858946","https://openalex.org/W2066315063","https://openalex.org/W2147242351","https://openalex.org/W2323053796","https://openalex.org/W4235989149","https://openalex.org/W4237625569","https://openalex.org/W4239720385"],"related_works":["https://openalex.org/W2047339154","https://openalex.org/W2323886274","https://openalex.org/W4214831444","https://openalex.org/W2027586194","https://openalex.org/W2055381384","https://openalex.org/W2091827946","https://openalex.org/W2093739742","https://openalex.org/W2065440767","https://openalex.org/W2339451782","https://openalex.org/W1555496119"],"abstract_inverted_index":{"We":[0],"show":[1,44],"that":[2,45,80],"the":[3,19,32,53],"property":[4],"of":[5,10,21,29,31,38,55,61,71,90,98],"sequential":[6],"compactness":[7],"for":[8,67,81],"subspaces":[9,37],"\ud835\udd49":[11,39],"is":[12,52,75,86],"countably":[13],"productive":[14],"in":[15,18],"ZF.":[16],"Also,":[17],"language":[20],"weak":[22],"choice":[23],"principles,":[24],"we":[25,43],"give":[26],"a":[27,56,76,87],"list":[28],"characterizations":[30],"topological":[33],"statement":[34],"'sequentially":[35],"compact":[36],"are":[40,102],"compact'.":[41],"Furthermore,":[42],"forms":[46],"152":[47],"(=":[48,66],"every":[49,68],"non-well-orderable":[50],"set":[51],"union":[54],"pairwise":[57],"disjoint":[58],"well-orderable":[59],"family":[60,69],"denumerable":[62],"sets)":[63],"and":[64,92,100],"214":[65],"A":[70],"infinite":[72],"sets":[73],"there":[74],"function":[77],"f":[78],"such":[79],"all":[82],"y\u220a":[83],"A,":[84],"f(y)":[85,94],"nonempty":[88],"subset":[89],"y":[91],"\u2223":[93,95],"=":[96],"\u05d0\u2080)":[97],"Howard":[99],"Rubin":[101],"equivalent.":[103]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}