C-open Sets on Topological Spaces
General Topology
2023-05-08 v1
Abstract
An open (resp., closed) subset A of a topological space (X, T ) is called C-open (resp., C-closed) set if cl(A) \ A (resp., A \ int(A)) is a countable set. This paper aims to present the concept of C-open and C-closed sets. We first investigate their basic properties. Then, we found some operators such as interior, closure, limit, border, and frontier using C-open and C-closed sets. The relationships between them are clarified and discussed. Finally, we exhibit continuous maps and compact space defined using C-open and C-closed sets and scrutinize their main properties.
Cite
@article{arxiv.2305.03166,
title = {C-open Sets on Topological Spaces},
author = {M. H. Alqahtani},
journal= {arXiv preprint arXiv:2305.03166},
year = {2023}
}