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Some topological properties of topological rough groups
- Source :
- Soft Computing. 25:3441-3453
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- 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.<br />19 pages
- Subjects :
- 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
Subjects
Details
- ISSN :
- 14337479 and 14327643
- Volume :
- 25
- Database :
- OpenAIRE
- Journal :
- Soft Computing
- Accession number :
- edsair.doi.dedup.....1082ff6945bc97306eea58831558bc57