Matches in SemOpenAlex for { <https://semopenalex.org/work/W2170069319> ?p ?o ?g. }
Showing items 1 to 76 of
76
with 100 items per page.
- W2170069319 endingPage "528" @default.
- W2170069319 startingPage "521" @default.
- W2170069319 abstract "The Splitting Theorem says that any given Hamel basis for a (Hausdorff) barrelled space E determines topologically complementary subspaces E c and E D , and that E c is flat, that is, contains no proper dense subspace. By use of this device it was shown that if E is non-flat it must contain a dense subspace of codimension at least ℵ 0 ; here we maximally increase the estimate to ℵ 1 under the assumption that the dominating cardinal ∂ equals ℵ 1 [strictly weaker than the Continuum Hypothesis (CH)]. A related assumption strictly weaker than the Generalised CH allows us to prove that E D is fit, that is, contains a dense subspace whose codimension in E D is dim ( E D ), the largest imaginable. Thus the two components are extreme opposites, and E itself is fit if and only if dim ( E D ) ≥ dim ( E c ), in which case there is a choice of basis for which E D = E . Morover, E is non-flat (if and) only if the codimension of E ′ is at least in E *. These results ensure latitude in the search for certain subspaces of E* transverse to E ′, as in the barrelled countable enlargement (BCE) problem, and show that every non-flat GM -space has a BCE." @default.
- W2170069319 created "2016-06-24" @default.
- W2170069319 creator A5073931154 @default.
- W2170069319 creator A5083948610 @default.
- W2170069319 date "1995-06-01" @default.
- W2170069319 modified "2023-10-02" @default.
- W2170069319 title "The fit and flat components of barrelled spaces" @default.
- W2170069319 cites W2022220699 @default.
- W2170069319 cites W2041995172 @default.
- W2170069319 cites W2099768441 @default.
- W2170069319 cites W2503186209 @default.
- W2170069319 cites W4231015384 @default.
- W2170069319 doi "https://doi.org/10.1017/s0004972700014374" @default.
- W2170069319 hasPublicationYear "1995" @default.
- W2170069319 type Work @default.
- W2170069319 sameAs 2170069319 @default.
- W2170069319 citedByCount "13" @default.
- W2170069319 countsByYear W21700693192013 @default.
- W2170069319 countsByYear W21700693192014 @default.
- W2170069319 countsByYear W21700693192016 @default.
- W2170069319 countsByYear W21700693192018 @default.
- W2170069319 countsByYear W21700693192020 @default.
- W2170069319 countsByYear W21700693192023 @default.
- W2170069319 crossrefType "journal-article" @default.
- W2170069319 hasAuthorship W2170069319A5073931154 @default.
- W2170069319 hasAuthorship W2170069319A5083948610 @default.
- W2170069319 hasBestOaLocation W21700693191 @default.
- W2170069319 hasConcept C110729354 @default.
- W2170069319 hasConcept C114614502 @default.
- W2170069319 hasConcept C12362212 @default.
- W2170069319 hasConcept C12426560 @default.
- W2170069319 hasConcept C134306372 @default.
- W2170069319 hasConcept C138885662 @default.
- W2170069319 hasConcept C191399826 @default.
- W2170069319 hasConcept C202444582 @default.
- W2170069319 hasConcept C2524010 @default.
- W2170069319 hasConcept C2778572836 @default.
- W2170069319 hasConcept C32834561 @default.
- W2170069319 hasConcept C33923547 @default.
- W2170069319 hasConcept C41895202 @default.
- W2170069319 hasConcept C83979697 @default.
- W2170069319 hasConceptScore W2170069319C110729354 @default.
- W2170069319 hasConceptScore W2170069319C114614502 @default.
- W2170069319 hasConceptScore W2170069319C12362212 @default.
- W2170069319 hasConceptScore W2170069319C12426560 @default.
- W2170069319 hasConceptScore W2170069319C134306372 @default.
- W2170069319 hasConceptScore W2170069319C138885662 @default.
- W2170069319 hasConceptScore W2170069319C191399826 @default.
- W2170069319 hasConceptScore W2170069319C202444582 @default.
- W2170069319 hasConceptScore W2170069319C2524010 @default.
- W2170069319 hasConceptScore W2170069319C2778572836 @default.
- W2170069319 hasConceptScore W2170069319C32834561 @default.
- W2170069319 hasConceptScore W2170069319C33923547 @default.
- W2170069319 hasConceptScore W2170069319C41895202 @default.
- W2170069319 hasConceptScore W2170069319C83979697 @default.
- W2170069319 hasIssue "3" @default.
- W2170069319 hasLocation W21700693191 @default.
- W2170069319 hasOpenAccess W2170069319 @default.
- W2170069319 hasPrimaryLocation W21700693191 @default.
- W2170069319 hasRelatedWork W1548358260 @default.
- W2170069319 hasRelatedWork W1601171442 @default.
- W2170069319 hasRelatedWork W1618082455 @default.
- W2170069319 hasRelatedWork W1985684185 @default.
- W2170069319 hasRelatedWork W2014627823 @default.
- W2170069319 hasRelatedWork W2121933206 @default.
- W2170069319 hasRelatedWork W2123465729 @default.
- W2170069319 hasRelatedWork W2996236851 @default.
- W2170069319 hasRelatedWork W4213271400 @default.
- W2170069319 hasRelatedWork W4221111274 @default.
- W2170069319 hasVolume "51" @default.
- W2170069319 isParatext "false" @default.
- W2170069319 isRetracted "false" @default.
- W2170069319 magId "2170069319" @default.
- W2170069319 workType "article" @default.