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If Cp(X) is strongly dominated by a second countable space, then X is countable.
- Source :
-
Journal of Mathematical Analysis & Applications . Oct2017, Vol. 454 Issue 2, p533-541. 9p. - Publication Year :
- 2017
-
Abstract
- We establish that a Tychonoff space X is countable if and only if C p ( X ) is strongly dominated by a second countable space. The same is true for a compact space K such that C p ( K , [ 0 , 1 ] ) is strongly dominated by a second countable space. We also prove that strong domination by a second countable space of the complement of the diagonal of a Tychonoff space X implies that X is an ℵ 0 -space. Our results solve several published open questions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 454
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 123428808
- Full Text :
- https://doi.org/10.1016/j.jmaa.2017.05.024