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2023•European Journal of Pure and Applied MathematicsOpen access

F−open and F−closed sets in Topological Spaces

Mesfer H. Alqahtani

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Abstract

An open (resp., closed) subset A of a topological space (X, T ) is called F-open (resp., F-closed) set if cl(A)\A (resp., A\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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What this paper is about

An open (resp., closed) subset A of a topological space (X, T ) is called F-open (resp., F-closed) set if cl(A)\A (resp., A\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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Available abstract

An open (resp., closed) subset A of a topological space (X, T ) is called F-open (resp., F-closed) set if cl(A)\A (resp., A\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.

Key concepts: Closed set, Mathematics, Open set, Closure (psychology), Topological space, Open and closed maps, Space (punctuation), Set (abstract data type)

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