Compactification of spaces of measures and pseudocompactness
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914726002294784 |
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| author | Bogachev, Vladimir I. |
| author_facet | Bogachev, Vladimir I. |
| contents | We prove pseudocompactness of a Tychonoff space $X$ and the space $\mathcal{P}(X)$ of Radon probability measures on it with the weak topology under the condition that the Stone-Čech compactification of the space $\mathcal{P}(X)$ is homeomorphic to the space $\mathcal{P}(βX)$ of Radon probability measures on the Stone-Čech compactification of the space~$X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15573 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compactification of spaces of measures and pseudocompactness Bogachev, Vladimir I. Functional Analysis 28A33, 54D35 We prove pseudocompactness of a Tychonoff space $X$ and the space $\mathcal{P}(X)$ of Radon probability measures on it with the weak topology under the condition that the Stone-Čech compactification of the space $\mathcal{P}(X)$ is homeomorphic to the space $\mathcal{P}(βX)$ of Radon probability measures on the Stone-Čech compactification of the space~$X$. |
| title | Compactification of spaces of measures and pseudocompactness |
| topic | Functional Analysis 28A33, 54D35 |
| url | https://arxiv.org/abs/2403.15573 |