Linear equivalence of (pseudo)compact spaces
| Autor: | Baars, Jan, van Mill, Jan, Tkachuk, Vladimir V. |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Quaestiones Mathematicae; Vol. 46 No. 3 (2023); 513-518 |
| ISSN: | 1607-3606 1727-933X |
| Popis: | 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 C*p(X) and C*p(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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|