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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2502.00570 |
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| _version_ | 1866913674008985600 |
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| author | Reznichenko, Evgenii Tkachenko, Mikhail |
| author_facet | Reznichenko, Evgenii Tkachenko, Mikhail |
| contents | An example of an infinite regular feebly compact quasitopological group is presented such that all continuous real-valued functions on the group are constant. The example is based on the use of Korovin orbits in $X^G$, where $X$ is a special regular countably compact space constructed by S.Bardyla and L.Zdomskyy and $G$ is an abstract Abelian group of an appropriate cardinality. Also, we study the interplay between the separation properties of the space $X$ and Korovin orbits in $X^G$. We show in particular that if $X$ contains two nonempty disjoint open subsets, then every Korovin orbit in $X^G$ is Hausdorff. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00570 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regular rigid Korovin orbits Reznichenko, Evgenii Tkachenko, Mikhail General Topology 22A30, 54H15, 54A25, 54C45 An example of an infinite regular feebly compact quasitopological group is presented such that all continuous real-valued functions on the group are constant. The example is based on the use of Korovin orbits in $X^G$, where $X$ is a special regular countably compact space constructed by S.Bardyla and L.Zdomskyy and $G$ is an abstract Abelian group of an appropriate cardinality. Also, we study the interplay between the separation properties of the space $X$ and Korovin orbits in $X^G$. We show in particular that if $X$ contains two nonempty disjoint open subsets, then every Korovin orbit in $X^G$ is Hausdorff. |
| title | Regular rigid Korovin orbits |
| topic | General Topology 22A30, 54H15, 54A25, 54C45 |
| url | https://arxiv.org/abs/2502.00570 |