Some topological properties of topological rough groups

Autor: Jinjin Li, Yujin Lin, Qianqian Sun, Fucai Lin
Rok vydání: 2021
Předmět:
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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