Matches in SemOpenAlex for { <https://semopenalex.org/work/W2022100303> ?p ?o ?g. }
Showing items 1 to 39 of
39
with 100 items per page.
- W2022100303 endingPage "281" @default.
- W2022100303 startingPage "281" @default.
- W2022100303 abstract "Received by the editors August 8, 1960 and, in revised form, February 8, 1961. 1 Supported by grants from the O.N.R., the N.S.F., and the Guggenheim Foundation. 2 Added in Proof. Paul Erd6s has kindly pointed out that a theorem equivalent to Theorem 1.1 was obtained by him and R. Rado in [Intersection theorems for systems of sets, J. London Math. Soc. 35 (1960), 85-90, Theorem I (ii)]. Their proof, while actually yielding some information even for finite cardinals r, is much longer than the one given here, which provided a reason for going ahead with the publication of this paper. Sanin's principal application of his result was to show [4; 5] that, for infinite cardinals r, the following topological property S(r) is preserved under arbitrary cartesian products: Every collection of open sets of cardinality >r has a subcollection of cardinality >r with nonempty intersection. (This need only be shown for open cubes, where it is first proved for finite products, after which the general case is proved like our Theorem 1.2.) For S(Ro) (which is weaker than separability, although equivalent to it in metric spaces), Sanin's theorem should be compared with the results in [1]." @default.
- W2022100303 created "2016-06-24" @default.
- W2022100303 creator A5067321132 @default.
- W2022100303 date "1962-02-01" @default.
- W2022100303 modified "2023-10-14" @default.
- W2022100303 title "A note on intersections" @default.
- W2022100303 cites W795440805 @default.
- W2022100303 doi "https://doi.org/10.1090/s0002-9939-1962-0133236-4" @default.
- W2022100303 hasPublicationYear "1962" @default.
- W2022100303 type Work @default.
- W2022100303 sameAs 2022100303 @default.
- W2022100303 citedByCount "8" @default.
- W2022100303 countsByYear W20221003032012 @default.
- W2022100303 crossrefType "journal-article" @default.
- W2022100303 hasAuthorship W2022100303A5067321132 @default.
- W2022100303 hasBestOaLocation W20221003031 @default.
- W2022100303 hasConcept C41008148 @default.
- W2022100303 hasConceptScore W2022100303C41008148 @default.
- W2022100303 hasIssue "2" @default.
- W2022100303 hasLocation W20221003031 @default.
- W2022100303 hasOpenAccess W2022100303 @default.
- W2022100303 hasPrimaryLocation W20221003031 @default.
- W2022100303 hasRelatedWork W2096946506 @default.
- W2022100303 hasRelatedWork W2130043461 @default.
- W2022100303 hasRelatedWork W2350741829 @default.
- W2022100303 hasRelatedWork W2358668433 @default.
- W2022100303 hasRelatedWork W2376932109 @default.
- W2022100303 hasRelatedWork W2382290278 @default.
- W2022100303 hasRelatedWork W2390279801 @default.
- W2022100303 hasRelatedWork W2748952813 @default.
- W2022100303 hasRelatedWork W2899084033 @default.
- W2022100303 hasRelatedWork W3004735627 @default.
- W2022100303 hasVolume "13" @default.
- W2022100303 isParatext "false" @default.
- W2022100303 isRetracted "false" @default.
- W2022100303 magId "2022100303" @default.
- W2022100303 workType "article" @default.