Matches in SemOpenAlex for { <https://semopenalex.org/work/W2018983676> ?p ?o ?g. }
Showing items 1 to 89 of
89
with 100 items per page.
- W2018983676 endingPage "3326" @default.
- W2018983676 startingPage "3319" @default.
- W2018983676 abstract "For a cardinal κ>1, a space X=(X,T) is κ-resolvable if X admits κ-many pairwise disjoint T-dense subsets; (X,T) is exactly κ-resolvable if it is κ-resolvable but not κ+-resolvable. The present paper complements and supplements the authorsʼ earlier work, which showed for suitably restricted spaces (X,T) and cardinals κ⩾λ⩾ω that (X,T), if κ-resolvable, admits an expansion U⊇T, with (X,U) Tychonoff if (X,T) is Tychonoff, such that (X,U) is μ-resolvable for all μ<λ but is not λ-resolvable (cf. Comfort and Hu, 2010 [11, Theorem 3.3]). Here the “finite case” is addressed. The authors show in ZFC for 1<n<ω: (a) every n-resolvable space (X,T) admits an exactly n-resolvable expansion U⊇T; (b) in some cases, even with (X,T) Tychonoff, no choice of U is available such that (X,U) is regular (nor even quasi-regular); (c) if regular and n-resolvable, (X,T) admits an exactly n-resolvable regular expansion U if and only if either (X,T) is itself exactly n-resolvable or (X,T) has a subspace which is either n-resolvable and nowhere dense or is (2n)-resolvable. In particular, every ω-resolvable regular space admits an exactly n-resolvable regular expansion. Further, for many familiar topological properties P (e.g., Tychonoff; has a clopen basis), one may choose U so that (X,U)∈P if (X,T)∈P." @default.
- W2018983676 created "2016-06-24" @default.
- W2018983676 creator A5068896912 @default.
- W2018983676 creator A5077437540 @default.
- W2018983676 date "2012-09-01" @default.
- W2018983676 modified "2023-09-29" @default.
- W2018983676 title "Exactly n-resolvable topological expansions" @default.
- W2018983676 cites W1503787111 @default.
- W2018983676 cites W1523058355 @default.
- W2018983676 cites W1535290843 @default.
- W2018983676 cites W1586359853 @default.
- W2018983676 cites W1597125013 @default.
- W2018983676 cites W1598063872 @default.
- W2018983676 cites W1963914286 @default.
- W2018983676 cites W1990720948 @default.
- W2018983676 cites W2043468215 @default.
- W2018983676 cites W2044313497 @default.
- W2018983676 cites W2045944529 @default.
- W2018983676 cites W2047704456 @default.
- W2018983676 cites W2052866841 @default.
- W2018983676 cites W2057233825 @default.
- W2018983676 cites W2077562214 @default.
- W2018983676 cites W2090339814 @default.
- W2018983676 cites W575797287 @default.
- W2018983676 doi "https://doi.org/10.1016/j.topol.2012.07.012" @default.
- W2018983676 hasPublicationYear "2012" @default.
- W2018983676 type Work @default.
- W2018983676 sameAs 2018983676 @default.
- W2018983676 citedByCount "2" @default.
- W2018983676 countsByYear W20189836762018 @default.
- W2018983676 crossrefType "journal-article" @default.
- W2018983676 hasAuthorship W2018983676A5068896912 @default.
- W2018983676 hasAuthorship W2018983676A5077437540 @default.
- W2018983676 hasBestOaLocation W20189836761 @default.
- W2018983676 hasConcept C114614502 @default.
- W2018983676 hasConcept C118615104 @default.
- W2018983676 hasConcept C134306372 @default.
- W2018983676 hasConcept C138885662 @default.
- W2018983676 hasConcept C17327563 @default.
- W2018983676 hasConcept C177264268 @default.
- W2018983676 hasConcept C191399826 @default.
- W2018983676 hasConcept C199360897 @default.
- W2018983676 hasConcept C2778572836 @default.
- W2018983676 hasConcept C32834561 @default.
- W2018983676 hasConcept C33923547 @default.
- W2018983676 hasConcept C41008148 @default.
- W2018983676 hasConcept C41895202 @default.
- W2018983676 hasConcept C43494777 @default.
- W2018983676 hasConcept C45340560 @default.
- W2018983676 hasConcept C87142424 @default.
- W2018983676 hasConceptScore W2018983676C114614502 @default.
- W2018983676 hasConceptScore W2018983676C118615104 @default.
- W2018983676 hasConceptScore W2018983676C134306372 @default.
- W2018983676 hasConceptScore W2018983676C138885662 @default.
- W2018983676 hasConceptScore W2018983676C17327563 @default.
- W2018983676 hasConceptScore W2018983676C177264268 @default.
- W2018983676 hasConceptScore W2018983676C191399826 @default.
- W2018983676 hasConceptScore W2018983676C199360897 @default.
- W2018983676 hasConceptScore W2018983676C2778572836 @default.
- W2018983676 hasConceptScore W2018983676C32834561 @default.
- W2018983676 hasConceptScore W2018983676C33923547 @default.
- W2018983676 hasConceptScore W2018983676C41008148 @default.
- W2018983676 hasConceptScore W2018983676C41895202 @default.
- W2018983676 hasConceptScore W2018983676C43494777 @default.
- W2018983676 hasConceptScore W2018983676C45340560 @default.
- W2018983676 hasConceptScore W2018983676C87142424 @default.
- W2018983676 hasIssue "15" @default.
- W2018983676 hasLocation W20189836761 @default.
- W2018983676 hasLocation W20189836762 @default.
- W2018983676 hasLocation W20189836763 @default.
- W2018983676 hasOpenAccess W2018983676 @default.
- W2018983676 hasPrimaryLocation W20189836761 @default.
- W2018983676 hasRelatedWork W1127009710 @default.
- W2018983676 hasRelatedWork W1985684185 @default.
- W2018983676 hasRelatedWork W1992861135 @default.
- W2018983676 hasRelatedWork W2064750418 @default.
- W2018983676 hasRelatedWork W2065891463 @default.
- W2018983676 hasRelatedWork W2072643132 @default.
- W2018983676 hasRelatedWork W2482260433 @default.
- W2018983676 hasRelatedWork W2793304552 @default.
- W2018983676 hasRelatedWork W4303438499 @default.
- W2018983676 hasRelatedWork W994366045 @default.
- W2018983676 hasVolume "159" @default.
- W2018983676 isParatext "false" @default.
- W2018983676 isRetracted "false" @default.
- W2018983676 magId "2018983676" @default.
- W2018983676 workType "article" @default.