{"id":"https://openalex.org/W7221112924","doi":"https://doi.org/10.48550/arxiv.2610.11066","title":"A Counterexample to Two Compactness Conjectures of Brudnyi","display_name":"A Counterexample to Two Compactness Conjectures of Brudnyi","publication_year":2026,"publication_date":"2026-10-08","ids":{"openalex":"https://openalex.org/W7221112924","doi":"https://doi.org/10.48550/arxiv.2610.11066"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.11066","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.11066","pdf_url":"https://arxiv.org/pdf/2610.11066","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.11066","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158229406","display_name":"Jinghao Huang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Jinghao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5158020152","display_name":"Ran Xu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu, Ran","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.9970999956130981,"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"}},"topics":[{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.9970999956130981,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.0012000000569969416,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bounded-sequences","display_name":"bounded sequences","score":0.5450000166893005},{"id":"https://openalex.org/keywords/compact-support","display_name":"compact support","score":0.6290000081062317},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.828000009059906}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.9574999809265137},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.8263999819755554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7664999961853027},{"id":"https://openalex.org/C182539199","wikidata":"https://www.wikidata.org/wiki/Q249092","display_name":"Equicontinuity","level":2,"score":0.6546000242233276},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6492000222206116},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.49869999289512634},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.49729999899864197},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4577000141143799},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.44020000100135803},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41990000009536743},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.41110000014305115},{"id":"https://openalex.org/C2778199601","wikidata":"https://www.wikidata.org/wiki/Q5165476","display_name":"Continuous function (set theory)","level":3,"score":0.40709999203681946},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.40700000524520874},{"id":"https://openalex.org/C43994743","wikidata":"https://www.wikidata.org/wiki/Q516776","display_name":"Measurable function","level":3,"score":0.40689998865127563},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3917999863624573},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3822000026702881},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.37869998812675476},{"id":"https://openalex.org/C129301229","wikidata":"https://www.wikidata.org/wiki/Q741865","display_name":"Uniform continuity","level":3,"score":0.34540000557899475},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C48421718","wikidata":"https://www.wikidata.org/wiki/Q5165477","display_name":"Continuous functions on a compact Hausdorff space","level":3,"score":0.25859999656677246},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.2574999928474426}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.11066","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.11066","pdf_url":"https://arxiv.org/pdf/2610.11066","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.11066","doi":"https://doi.org/10.48550/arxiv.2610.11066","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.11066","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.11066","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.11066","pdf_url":"https://arxiv.org/pdf/2610.11066","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221112924.pdf","grobid_xml":"https://content.openalex.org/works/W7221112924.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2316663115","https://openalex.org/W4300877683","https://openalex.org/W7165880482","https://openalex.org/W1036127759","https://openalex.org/W1992073786","https://openalex.org/W4205976234","https://openalex.org/W1510695753","https://openalex.org/W3016755807","https://openalex.org/W7100709811","https://openalex.org/W2085250260"],"abstract_inverted_index":{"We":[0],"construct":[1],"a":[2,23,42],"quasi-Banach":[3],"function":[4],"lattice":[5],"$X$":[6,21,34],"on":[7],"$\\mathbb":[8],"R$":[9],"whose":[10],"quasi-norm":[11],"is":[12,31],"order":[13],"continuous":[14],"and":[15,35,47],"invariant":[16],"under":[17],"every":[18],"translation.":[19],"Nevertheless,":[20],"contains":[22],"bounded":[24],"sequence":[25],"with":[26],"common":[27],"compact":[28],"support":[29],"which":[30],"equicontinuous":[32],"in":[33,52],"has":[36],"no":[37],"norm-convergent":[38],"subsequence.":[39],"This":[40],"provides":[41],"counterexample":[43],"to":[44],"Conjectures":[45],"2.5":[46],"2.11":[48],"proposed":[49],"by":[50],"Brudnyi":[51],"\\cite{Brudnyi2015}.":[53]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-10T00:00:00"}
