On uniformly continuous surjections between function spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908481154449408 |
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| author | Eysen, Ali Emre Valov, Vesko |
| author_facet | Eysen, Ali Emre Valov, Vesko |
| contents | We consider uniformly continuous surjections between $C_p(X)$ and $C_p(Y)$ (resp, $C_p^*(X)$ and $C_p^*(Y$)) and show that if $X$ has some dimensional-like properties, then so does $Y$. In particular, we prove that if $T:C_p(X)\to C_p(Y)$ is a continuous linear surjection, then $\dim Y=0$ if $\dim X=0$. This provides a positive answer to a question raised by Kawamura-Leiderman \cite[Problem 3.1]{kl}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00542 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On uniformly continuous surjections between function spaces Eysen, Ali Emre Valov, Vesko General Topology 54C35 We consider uniformly continuous surjections between $C_p(X)$ and $C_p(Y)$ (resp, $C_p^*(X)$ and $C_p^*(Y$)) and show that if $X$ has some dimensional-like properties, then so does $Y$. In particular, we prove that if $T:C_p(X)\to C_p(Y)$ is a continuous linear surjection, then $\dim Y=0$ if $\dim X=0$. This provides a positive answer to a question raised by Kawamura-Leiderman \cite[Problem 3.1]{kl}. |
| title | On uniformly continuous surjections between function spaces |
| topic | General Topology 54C35 |
| url | https://arxiv.org/abs/2404.00542 |