TY - JOUR
TI - $F-$open and $F-$closed sets in Topological Spaces
PY - 2023/04/30
Y2 - 2024/04/24
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 16
IS - 2
DO - 10.29020/nybg.ejpam.v16i2.4583
UR - https://doi.org/10.29020/nybg.ejpam.v16i2.4583
SP - 819-832
AB - 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.
ER -