{"id":"https://openalex.org/W2125884025","doi":"https://doi.org/10.1007/978-3-540-39966-7_1","title":"Topological Digital Topology","display_name":"Topological Digital Topology","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2125884025","doi":"https://doi.org/10.1007/978-3-540-39966-7_1","mag":"2125884025"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-39966-7_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-540-39966-7_1","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-540-39966-7_1.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-540-39966-7_1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042305769","display_name":"Ralph Kopperman","orcid":null},"institutions":[{"id":"https://openalex.org/I125687163","display_name":"City College of New York","ror":"https://ror.org/00wmhkr98","country_code":"US","type":"education","lineage":["https://openalex.org/I125687163"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ralph Kopperman","raw_affiliation_strings":["Department of Mathematics, City College of New York, New York, NY, 10031, USA","City College of New York ,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City College of New York, New York, NY, 10031, USA","institution_ids":["https://openalex.org/I125687163"]},{"raw_affiliation_string":"City College of New York ,","institution_ids":["https://openalex.org/I125687163"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5042305769"],"corresponding_institution_ids":["https://openalex.org/I125687163"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.6847,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.67972811,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9279999732971191,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/hausdorff-space","display_name":"Hausdorff space","score":0.7619433403015137},{"id":"https://openalex.org/keywords/compact-open-topology","display_name":"Compact-open topology","score":0.7574266195297241},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.6893415451049805},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.6712422370910645},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5639129877090454},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5444170236587524},{"id":"https://openalex.org/keywords/digital-topology","display_name":"Digital topology","score":0.509619951248169},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4513801336288452},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4512759745121002},{"id":"https://openalex.org/keywords/topological-vector-space","display_name":"Topological vector space","score":0.4318719804286957},{"id":"https://openalex.org/keywords/general-topology","display_name":"General topology","score":0.40711310505867004},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3655853867530823},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3546866774559021},{"id":"https://openalex.org/keywords/topological-tensor-product","display_name":"Topological tensor product","score":0.3177722692489624},{"id":"https://openalex.org/keywords/extension-topology","display_name":"Extension topology","score":0.16477853059768677},{"id":"https://openalex.org/keywords/functional-analysis","display_name":"Functional analysis","score":0.16266271471977234},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14485231041908264},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1159018874168396}],"concepts":[{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.7619433403015137},{"id":"https://openalex.org/C6419321","wikidata":"https://www.wikidata.org/wiki/Q1669863","display_name":"Compact-open topology","level":5,"score":0.7574266195297241},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.6893415451049805},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.6712422370910645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5639129877090454},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5444170236587524},{"id":"https://openalex.org/C557022819","wikidata":"https://www.wikidata.org/wiki/Q5276205","display_name":"Digital topology","level":5,"score":0.509619951248169},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4513801336288452},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4512759745121002},{"id":"https://openalex.org/C47776270","wikidata":"https://www.wikidata.org/wiki/Q1455249","display_name":"Topological vector space","level":3,"score":0.4318719804286957},{"id":"https://openalex.org/C129089157","wikidata":"https://www.wikidata.org/wiki/Q621550","display_name":"General topology","level":3,"score":0.40711310505867004},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3655853867530823},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3546866774559021},{"id":"https://openalex.org/C178099376","wikidata":"https://www.wikidata.org/wiki/Q7825044","display_name":"Topological tensor product","level":4,"score":0.3177722692489624},{"id":"https://openalex.org/C143913944","wikidata":"https://www.wikidata.org/wiki/Q5421952","display_name":"Extension topology","level":4,"score":0.16477853059768677},{"id":"https://openalex.org/C55112680","wikidata":"https://www.wikidata.org/wiki/Q190549","display_name":"Functional analysis","level":3,"score":0.16266271471977234},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14485231041908264},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1159018874168396},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-39966-7_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-540-39966-7_1","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-540-39966-7_1.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-540-39966-7_1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-540-39966-7_1","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-540-39966-7_1.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309102","display_name":"City University of New York","ror":"https://ror.org/00453a208"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2125884025.pdf","grobid_xml":"https://content.openalex.org/works/W2125884025.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1971980119","https://openalex.org/W1980612250","https://openalex.org/W1995215698","https://openalex.org/W2002713832","https://openalex.org/W2018797100","https://openalex.org/W2029812885","https://openalex.org/W2034418223","https://openalex.org/W2084887209","https://openalex.org/W2116593370","https://openalex.org/W2159682905","https://openalex.org/W2215918220","https://openalex.org/W2223797986","https://openalex.org/W2323810788","https://openalex.org/W4300857373"],"related_works":["https://openalex.org/W1987292769","https://openalex.org/W580130575","https://openalex.org/W99737357","https://openalex.org/W2056826558","https://openalex.org/W12550991","https://openalex.org/W4213175243","https://openalex.org/W2887137748","https://openalex.org/W3022742563","https://openalex.org/W2375255986","https://openalex.org/W4230385490"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
