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Linear equivalence of (pseudo) compact spaces.
- Source :
-
QM - Quaestiones Mathematicae . Apr2023, Vol. 46 Issue 3, p513-518. 6p. - Publication Year :
- 2023
-
Abstract
- Given Tychonoff spaces X and Y, Uspenskij proved in [15] that if X is pseudocompact and Cp(X) is uniformly homeomorphic to Cp(Y), then Y is also pseudocompact. In particular, if Cp(X) is linearly homeomorphic to Cp(Y), then X is pseudocompact if and only if so is Y. This easily implies Arhangel'skii's theorem [1] which states that, in the case when Cp(X) is linearly homeomorphic to Cp(Y the space X is compact if and only if Y is compact. We will establish that existence of a linear homeomorphism between the spaces Cp*(X) and Cp*(Y) implies that X is (pseudo)compact if and only if so is Y. We will also show that the methods of proof used by Arhangel'skii and Uspenskij do not work in our case. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16073606
- Volume :
- 46
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- QM - Quaestiones Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 163192083
- Full Text :
- https://doi.org/10.2989/16073606.2022.2034066