Properties of the space of group-valued continuous functions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909413324881920 |
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| author | Mishra, Sanjay Pandey, Pankaj Ravindran, Sreeram |
| author_facet | Mishra, Sanjay Pandey, Pankaj Ravindran, Sreeram |
| contents | In this paper, we find necessary and sufficient conditions for countable fan tightness and countable strong fan tightness of the space (briefly, $C_{p}(X,G)$) of all group-valued continuous functions endowed with the topology of pointwise convergence in term of Menger property and Rothberger property respectively. Furthermore, we establish a relationship between countable fan tightness, the Reznichenko property and the Hurewicz property for the space $C_{p}(X,G)$. In addition to this we prove that the Menger property is preserve during $G$-equivalence of topological spaces. Through this paper, we establish a general result regarding fan tightness of $C_{p}(X,G)$ and Hurewicz number of the space $X^{n}$ for every natural number $n$. Finally, we study the monolithicity of the space $C_{p}(X,G)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_02199 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Properties of the space of group-valued continuous functions Mishra, Sanjay Pandey, Pankaj Ravindran, Sreeram General Topology 54C35, 54A25 and 54H11 In this paper, we find necessary and sufficient conditions for countable fan tightness and countable strong fan tightness of the space (briefly, $C_{p}(X,G)$) of all group-valued continuous functions endowed with the topology of pointwise convergence in term of Menger property and Rothberger property respectively. Furthermore, we establish a relationship between countable fan tightness, the Reznichenko property and the Hurewicz property for the space $C_{p}(X,G)$. In addition to this we prove that the Menger property is preserve during $G$-equivalence of topological spaces. Through this paper, we establish a general result regarding fan tightness of $C_{p}(X,G)$ and Hurewicz number of the space $X^{n}$ for every natural number $n$. Finally, we study the monolithicity of the space $C_{p}(X,G)$. |
| title | Properties of the space of group-valued continuous functions |
| topic | General Topology 54C35, 54A25 and 54H11 |
| url | https://arxiv.org/abs/2412.02199 |