Semiflows on finite topological spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908305249533952 |
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| author | Chocano, Pedro J. |
| author_facet | Chocano, Pedro J. |
| contents | In this paper, we study flows and semiflows defined on any given finite topological $T_0$-space $X$. We show that there exist non-trivial semiflows on $X$, unless $X$ is a minimal finite space. Specifically, non-trivial semiflows exist if and only if $X$ contains down beat points, and a non-trivial semiflow is essentially a strong deformation retraction. As a consequence of this result, we provide a new and concise proof that the only flow that can be defined on $X$ is the trivial flow. Finally, we discuss the number of different semiflows that can be defined on $X$ in terms of down beat points and other special points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05175 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semiflows on finite topological spaces Chocano, Pedro J. General Topology In this paper, we study flows and semiflows defined on any given finite topological $T_0$-space $X$. We show that there exist non-trivial semiflows on $X$, unless $X$ is a minimal finite space. Specifically, non-trivial semiflows exist if and only if $X$ contains down beat points, and a non-trivial semiflow is essentially a strong deformation retraction. As a consequence of this result, we provide a new and concise proof that the only flow that can be defined on $X$ is the trivial flow. Finally, we discuss the number of different semiflows that can be defined on $X$ in terms of down beat points and other special points. |
| title | Semiflows on finite topological spaces |
| topic | General Topology |
| url | https://arxiv.org/abs/2504.05175 |