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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.05956 |
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| _version_ | 1866918047505186816 |
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| author | Maity, Sunil Kumar Paul, Monika |
| author_facet | Maity, Sunil Kumar Paul, Monika |
| contents | In this article, we construct a band of topological groups from a cryptogroup. Also, we prove that a band of topological groups is metrizable if and only if each $\mathcal{H}$-class is metrizable. Finally, we demonstrate that if $S$ is a band of topological groups and $N$ is a full normal subcryptogroup of $S$, then $S/N$ is Hausdorff if and only if $ρ_{_N}$ is closed in $S \times S$ if and, $ρ_{_N}$ is closed in $S \times S$ if and only if $N$ is closed in $S$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Band of topological groups Maity, Sunil Kumar Paul, Monika Group Theory General Topology In this article, we construct a band of topological groups from a cryptogroup. Also, we prove that a band of topological groups is metrizable if and only if each $\mathcal{H}$-class is metrizable. Finally, we demonstrate that if $S$ is a band of topological groups and $N$ is a full normal subcryptogroup of $S$, then $S/N$ is Hausdorff if and only if $ρ_{_N}$ is closed in $S \times S$ if and, $ρ_{_N}$ is closed in $S \times S$ if and only if $N$ is closed in $S$. |
| title | Band of topological groups |
| topic | Group Theory General Topology |
| url | https://arxiv.org/abs/2506.05956 |