Closed graph property and Khalimsky spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917883504754688 |
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| author | Pourattar, Mehrnaz Shirazi, Fatemah Ayatollah Zadeh Mardanbeigi, Mohammad Reza |
| author_facet | Pourattar, Mehrnaz Shirazi, Fatemah Ayatollah Zadeh Mardanbeigi, Mohammad Reza |
| contents | In the following text for Khalimsky $n-$dimensional space $\mathcal{K}^n$ we show self--map $f:\mathcal{K}^n\to\mathcal{K}^n$ has closed graph if and only if there exist integers $λ_1,\ldots,λ_n$ such that $f$ is a constant map with value $(2λ_1,\cdots,2λ_n)$. We also show each self--map on Khalimsky circle and Khalimsky sphere which has closed graph is a constant map. The text is motivated by examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02065 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Closed graph property and Khalimsky spaces Pourattar, Mehrnaz Shirazi, Fatemah Ayatollah Zadeh Mardanbeigi, Mohammad Reza General Topology 54C35, 54D05 In the following text for Khalimsky $n-$dimensional space $\mathcal{K}^n$ we show self--map $f:\mathcal{K}^n\to\mathcal{K}^n$ has closed graph if and only if there exist integers $λ_1,\ldots,λ_n$ such that $f$ is a constant map with value $(2λ_1,\cdots,2λ_n)$. We also show each self--map on Khalimsky circle and Khalimsky sphere which has closed graph is a constant map. The text is motivated by examples. |
| title | Closed graph property and Khalimsky spaces |
| topic | General Topology 54C35, 54D05 |
| url | https://arxiv.org/abs/2501.02065 |