Number versus size
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- by Stephen Watson PDF
- Proc. Amer. Math. Soc. 102 (1988), 761-764 Request permission
Abstract:
We show, for example, that normal collectionwise Hausdorff spaces which are collectionwise normal with respect to families of cardinality ${\aleph _1}$ are collectionwise normal with respect to any number of copies of $[0,1]$. We also show that normal collectionwise Hausdorff spaces are collectionwise normal with respect to scattered paracompact sets.References
- William G. Fleissner, A normal collectionwise Hausdorff, not collectionwise normal space, General Topology and Appl. 6 (1976), no. 1, 57–64. MR 391032 C. Navy, Nonparacompactness in Paralindelof spaces, Thesis, University of Wisconsin-Madison, 1981.
- R. Telgársky, Total paracompactness and paracompact dispersed spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 567–572 (English, with Russian summary). MR 235517
- Stephen Watson, Separation and coding, Trans. Amer. Math. Soc. 342 (1994), no. 1, 83–106. MR 1225576, DOI 10.1090/S0002-9947-1994-1225576-8
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 761-764
- MSC: Primary 54D15; Secondary 54A25, 54D10
- DOI: https://doi.org/10.1090/S0002-9939-1988-0929017-X
- MathSciNet review: 929017