Matches in SemOpenAlex for { <https://semopenalex.org/work/W1992682664> ?p ?o ?g. }
Showing items 1 to 73 of
73
with 100 items per page.
- W1992682664 abstract "Modifying a recent example obtained under the assumption of the Continuum Hypothesis by Michael Wage, we prove, without any settheoretic assumptions beyond ZFC, that for every natural number n there exists a separable and first countable space X such that: (a) Xn is Lindelof and dim Xn = 0; (b) Xn I I is normal but dim Xn > 0. We obtain from this the following corollary. There exists a separable and first countable Lindelof space X such that: (a) dim X = 0; (b) X2 is normal but dim X2 > 0. The space X instead of being Lindelof can be made locally compact and locally countable. Assuming the Continuum Hypothesis (CH) Michael Wage constructed a beautiful example of a strongly zerodimensional space X such that x2 is not strongly zerodimensional, thus giving a consistent negative answer to a long outstanding problem in dimension theory, namely, whether dim X x Y 0. COROLLARY. There exists a separable and first countable Lindelof space X such that: (a) dim X = 0; (b) X2 is normal but dim X2 > 0. Thus our theorem provides a real counterexample to the conjecture that dim X x Y < dim X + dim Y in the class of normal spaces. The space X, Received by the editors October 1, 1978. AMS (MOS) subject classifications (1970). Primary 54F45, 54B 10, 54D20." @default.
- W1992682664 created "2016-06-24" @default.
- W1992682664 creator A5084802338 @default.
- W1992682664 date "1979-02-01" @default.
- W1992682664 modified "2023-09-24" @default.
- W1992682664 title "On the dimension of product spaces and an example of M. Wage" @default.
- W1992682664 cites W1027757459 @default.
- W1992682664 cites W1511205498 @default.
- W1992682664 cites W2043643343 @default.
- W1992682664 cites W2324296705 @default.
- W1992682664 doi "https://doi.org/10.1090/s0002-9939-1979-0537097-3" @default.
- W1992682664 hasPublicationYear "1979" @default.
- W1992682664 type Work @default.
- W1992682664 sameAs 1992682664 @default.
- W1992682664 citedByCount "13" @default.
- W1992682664 crossrefType "journal-article" @default.
- W1992682664 hasAuthorship W1992682664A5084802338 @default.
- W1992682664 hasBestOaLocation W19926826641 @default.
- W1992682664 hasConcept C110729354 @default.
- W1992682664 hasConcept C114614502 @default.
- W1992682664 hasConcept C134306372 @default.
- W1992682664 hasConcept C138885662 @default.
- W1992682664 hasConcept C162838799 @default.
- W1992682664 hasConcept C202444582 @default.
- W1992682664 hasConcept C2778572836 @default.
- W1992682664 hasConcept C2780012671 @default.
- W1992682664 hasConcept C2780990831 @default.
- W1992682664 hasConcept C33676613 @default.
- W1992682664 hasConcept C33923547 @default.
- W1992682664 hasConcept C41895202 @default.
- W1992682664 hasConcept C70710897 @default.
- W1992682664 hasConcept C96488702 @default.
- W1992682664 hasConceptScore W1992682664C110729354 @default.
- W1992682664 hasConceptScore W1992682664C114614502 @default.
- W1992682664 hasConceptScore W1992682664C134306372 @default.
- W1992682664 hasConceptScore W1992682664C138885662 @default.
- W1992682664 hasConceptScore W1992682664C162838799 @default.
- W1992682664 hasConceptScore W1992682664C202444582 @default.
- W1992682664 hasConceptScore W1992682664C2778572836 @default.
- W1992682664 hasConceptScore W1992682664C2780012671 @default.
- W1992682664 hasConceptScore W1992682664C2780990831 @default.
- W1992682664 hasConceptScore W1992682664C33676613 @default.
- W1992682664 hasConceptScore W1992682664C33923547 @default.
- W1992682664 hasConceptScore W1992682664C41895202 @default.
- W1992682664 hasConceptScore W1992682664C70710897 @default.
- W1992682664 hasConceptScore W1992682664C96488702 @default.
- W1992682664 hasLocation W19926826641 @default.
- W1992682664 hasOpenAccess W1992682664 @default.
- W1992682664 hasPrimaryLocation W19926826641 @default.
- W1992682664 hasRelatedWork W1040710948 @default.
- W1992682664 hasRelatedWork W113994252 @default.
- W1992682664 hasRelatedWork W1621801769 @default.
- W1992682664 hasRelatedWork W1679412374 @default.
- W1992682664 hasRelatedWork W1714496748 @default.
- W1992682664 hasRelatedWork W1989203604 @default.
- W1992682664 hasRelatedWork W1997618817 @default.
- W1992682664 hasRelatedWork W2024874328 @default.
- W1992682664 hasRelatedWork W2043643343 @default.
- W1992682664 hasRelatedWork W2080845371 @default.
- W1992682664 hasRelatedWork W2083506033 @default.
- W1992682664 hasRelatedWork W2093092368 @default.
- W1992682664 hasRelatedWork W2151768269 @default.
- W1992682664 hasRelatedWork W2158766333 @default.
- W1992682664 hasRelatedWork W2283896744 @default.
- W1992682664 hasRelatedWork W2358093851 @default.
- W1992682664 hasRelatedWork W2561543329 @default.
- W1992682664 hasRelatedWork W605624406 @default.
- W1992682664 hasRelatedWork W90060193 @default.
- W1992682664 hasRelatedWork W2473673360 @default.
- W1992682664 isParatext "false" @default.
- W1992682664 isRetracted "false" @default.
- W1992682664 magId "1992682664" @default.
- W1992682664 workType "article" @default.