On (Λ, p)-closed Sets and the Related Notions in Topological spaces

Abstract

This article deals with the concepts of Λp-sets and (Λ, p)-closed sets which are defined by utilizing the notions of preopen sets and preclosed sets. We also introduce and characterize some new low separation axioms. Characterizations of Λp-R0 spaces are given. Moreover, we introduce the concept of weakly (Λ, p)-continuous functions. In particular, several characterizations of weakly (Λ, p)-continuous functions are established.

Weakly $\theta b(\Lambda,p)$-open Functions and Weakly $\theta b(\Lambda,p)$-closed Functions

“…The set of all (Λ, p)-cluster points of A is called the (Λ, p)-closure [6] of A and is denoted by A (Λ,p) . The union of all (Λ, p)-open sets of X contained in A is called the (Λ, p)-interior [6] of A and is denoted by A (Λ,p) . Let A be a subset of a topological space (X, τ ).…”

“…Let A be a subset of a topological space (X, τ ). The θ(Λ, p)-closure [6] of A, A θ(Λ,p) , is defined as follows:…”

Almost strong $\theta(\Lambda,p)$-continuity for Functions

“…The set of all (Λ, p)-cluster points of A is called the (Λ, p)-closure [6] of A and is denoted by A (Λ,p) . The union of all (Λ, p)-open sets of X contained in A is called the (Λ, p)-interior [6] of A and is denoted by A (Λ,p) . The θ(Λ, p)-closure [6] of A, A θ(Λ,p) , is defined as follows:…”

“…The union of all (Λ, p)-open sets of X contained in A is called the (Λ, p)-interior [6] of A and is denoted by A (Λ,p) . The θ(Λ, p)-closure [6] of A, A θ(Λ,p) , is defined as follows:…”

Characterizations of Almost (τ1, τ2)-Continuous Functions

“…Moreover, some characterizations of almost (Λ, s)-continuous functions were presented in [3]. In [4], the authors introduced and investigated the concept of weakly (Λ, p)-continuous functions.…”