On proper compactifications of topological groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918467804856320 |
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| author | Kozlov, K. L. Leiderman, A. G. |
| author_facet | Kozlov, K. L. Leiderman, A. G. |
| contents | In the present paper, we examine in detail the method of "graph compactifications" of topological groups. The graph and Ellis methods of constructing proper compactifications of topological groups are applied for the investigation of possible extensions of algebraic operations on a topological group to its compactifications, and give descriptions of Roelcke, Ellis, WAP, and graph compactifications of topological groups. Additionally, using dichotomy theorems of A.V.Arhangelskii, we show that the description of compactifications can be effectively used in the investigation of topological properties of their remainders. As examples, subgroups of the permutation group (in the permutation topology) and the automorphism group of a LOTS (in the topology of pointwise convergence) are examined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23201 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On proper compactifications of topological groups Kozlov, K. L. Leiderman, A. G. General Topology 57S05, 20E22, 22F05, 22F50, 54E05, 54D35 54H15, 47B02 In the present paper, we examine in detail the method of "graph compactifications" of topological groups. The graph and Ellis methods of constructing proper compactifications of topological groups are applied for the investigation of possible extensions of algebraic operations on a topological group to its compactifications, and give descriptions of Roelcke, Ellis, WAP, and graph compactifications of topological groups. Additionally, using dichotomy theorems of A.V.Arhangelskii, we show that the description of compactifications can be effectively used in the investigation of topological properties of their remainders. As examples, subgroups of the permutation group (in the permutation topology) and the automorphism group of a LOTS (in the topology of pointwise convergence) are examined. |
| title | On proper compactifications of topological groups |
| topic | General Topology 57S05, 20E22, 22F05, 22F50, 54E05, 54D35 54H15, 47B02 |
| url | https://arxiv.org/abs/2604.23201 |