Some topological properties of topological rough groups
Autor: | Jinjin Li, Yujin Lin, Qianqian Sun, Fucai Lin |
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Rok vydání: | 2021 |
Předmět: |
Physics
0209 industrial biotechnology Group (mathematics) General Topology (math.GN) Inverse Group Theory (math.GR) 02 engineering and technology Topology Space (mathematics) Theoretical Computer Science Separation axiom 020901 industrial engineering & automation Product (mathematics) FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Equivalence relation 020201 artificial intelligence & image processing Geometry and Topology Open mapping theorem (functional analysis) Identity element Mathematics - Group Theory Primary: 22A05 54A05. Secondary: 03E25 Software Mathematics - General Topology |
Zdroj: | Soft Computing. 25:3441-3453 |
ISSN: | 1433-7479 1432-7643 |
DOI: | 10.1007/s00500-021-05631-6 |
Popis: | Let $(U, R)$ be an approximation space with $U$ being non-empty set and $R$ being an equivalence relation on $U$, and let $\overline{G}$ and $\underline{G}$ be the upper approximation and the lower approximation of subset $G$ of $U$. A topological rough group $G$ is a rough group $G=(\underline{G}, \overline{G})$ endowed with a topology, which is induced from the upper approximation space $\overline{G}$, such that the product mapping $f: G\times G\rightarrow \overline{G}$ and the inverse mapping are continuous. In the class of topological rough groups, the relations of some separation axioms are obtained, some basic properties of the neighborhoods of the rough identity element and topological rough subgroups are investigated. In particular, some examples of topological rough groups are provided to clarify some facts about topological rough groups. Moreover, the version of open mapping theorem in the class of topological rough group is obtained. Further, some interesting open questions are posed. 19 pages |
Databáze: | OpenAIRE |
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