Characterizations of upper and lower \alpha(\mu_X,\mu_Y)-continuous multifunctions

Abstract

A new class of multifunctions, called upper (lower) α(µ X , µ Y )-continuous multifunctions, has been defined and studied. Some characterizations and several properties concerning upper (lower) α(µ X , µ Y )-continuous multifunctions are obtained.

Characterizations of $\delta p(\Lambda,s)$-$R_0$ Spaces

“…A point x of X is called a δ(Λ, s)-cluster point [21] ,s) ] (Λ,s) ̸ = ∅ for every (Λ, s)-open set V of X containing x. The set of all δ(Λ, s)-cluster points of A is called the δ(Λ, s)-closure [21] of A and is denoted by A δ(Λ,s) . If A = A δ(Λ,s) , then A is said to be δ(Λ, s)-closed [21].…”

“…Boonpok and Khampakdee [2] introduced and investigated the concepts of δs(Λ, s)-R 0 spaces and δs(Λ, s)-R 1 spaces. Quite recently, Srisarakham and Boonpok [21] defined and studied the notion of δp(Λ, s)-open sets in topological spaces. In this paper, we introduce the concept of δp(Λ, s)-R 0 spaces.…”

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

“…Chutiman and Boonpok [9] obtained several properties of weakly b(Λ, p)-open functions. Furthermore, some characterizations of weakly δ(Λ, p)-open functions and weakly δ(Λ, p)-closed functions were presented in [19] and [12], respectively. Klanarong and Boonpok [13] studied the notions of weakly s(Λ, p)-open functions and weakly s(Λ, p)-closed functions by utilizing s(Λ, p)-open sets and the s(Λ, p)-closure operator.…”

Properties of Weakly $\beta(\Lambda,p)$-open Functions and Weakly $\beta(\Lambda,p)$-closed Functions

“…Caldas and Navalagi [7] introduced two new classes of functions called weakly preopen functions and weakly preclosed functions as a generalization of weak openness and weak closedness due to [15] and [16], respectively. Moreover, Caldas and Navalagi [8] [17] studied several properties of δp(Λ, s)-closed sets and the δp(Λ, s)-closure operator. Khampakdee and Boonpok [11] introduced and investigated the concept of (Λ, p)-closed functions.…”

“…The notion of weakly b(Λ, p)-open functions was studied by Chutiman and Boonpok [9]. Some characterizations of weakly δ(Λ, p)-open functions and weakly δ(Λ, p)closed functions were presented in [18] and [12], respectively. Moreover, several characterizations θp(Λ, p)-open functions and θp(Λ, p)-closed functions were established in [2].…”