$G$-compactness for topological groups with operations
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866917697077379072 |
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| author | Mucuk, Osman Çakallı, Hüseyin |
| author_facet | Mucuk, Osman Çakallı, Hüseyin |
| contents | It is well known that for a Hausdorff topological group $X$, the limits of convergent sequences in $X$ define a function denoted by $\lim$ from the set of all convergent sequences in $X$ to $X$. This notion has been modified by Connor and Grosse-Erdmann for real functions by replacing $\lim$ with an arbitrary linear functional $G$ defined on a linear subspace of the vector space of all real sequences. Recently some authors have extended the concept to the topological group setting and introduced the concepts of $G$-continuity, $G$-compactness and $G$-connectedness. In this paper we prove some results on different types of $G$-compactness for topological group with operations which include topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras, and many others. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_07561 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | $G$-compactness for topological groups with operations Mucuk, Osman Çakallı, Hüseyin General Topology Algebraic Topology 40J05, 54A05, 22A05 It is well known that for a Hausdorff topological group $X$, the limits of convergent sequences in $X$ define a function denoted by $\lim$ from the set of all convergent sequences in $X$ to $X$. This notion has been modified by Connor and Grosse-Erdmann for real functions by replacing $\lim$ with an arbitrary linear functional $G$ defined on a linear subspace of the vector space of all real sequences. Recently some authors have extended the concept to the topological group setting and introduced the concepts of $G$-continuity, $G$-compactness and $G$-connectedness. In this paper we prove some results on different types of $G$-compactness for topological group with operations which include topological groups, topological rings without identity, R-modules, Lie algebras, Jordan algebras, and many others. |
| title | $G$-compactness for topological groups with operations |
| topic | General Topology Algebraic Topology 40J05, 54A05, 22A05 |
| url | https://arxiv.org/abs/2012.07561 |