$F-$open and $F-$closed sets in Topological Spaces

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i2.4583

Keywords:

Isomorphic Graphs; Alexandroff Topology; Topological Properties.

Abstract

An open (resp., closed) subset $A$ of a topological space $(X, \mathcal{T})$ is called {\it $F$-open} (resp., $F$-closed) set if $ cl(A)\setminus A $ (resp., $ A\setminus int(A) $) is finite set. In this work, we study the main properties of these definitions and examine the relationships between $F$-open and $F$-closed sets with other kinds such as regularly open, regularly closed, closed, and open sets. Then, we establish some operators such as $F$-interior, $F$-closure, and $F$-derived...etc., using $F$-open and $F$-closed sets. At the end of this work, we introduce definitions of $F$-continuous function, $F$-compact space, and other related properties.

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Published

2023-04-30

Issue

Section

Nonlinear Analysis

How to Cite

$F-$open and $F-$closed sets in Topological Spaces. (2023). European Journal of Pure and Applied Mathematics, 16(2), 819-832. https://doi.org/10.29020/nybg.ejpam.v16i2.4583

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