Connectedness and Compactness via Semi-Star-Alpha-Open Sets

Abstract

In this paper, we introduce new concepts, namely semi*α-connectedness and semi*αcompactness using semi*α-open sets. We investigate their basic properties. We also discuss their relationships with already existing concepts of connectedness and compactness.

THEORY OF GENERALIZED CONNECTEDNESS (g-Tg-CONNECTEDNESS) IN GENERALIZED TOPOLOGICAL SPACES (Tg-SPACES)

“…Indeed, T-connectedness is an absolute property of a T-set [1,4,5], and g-T-connectedness, T g -connectedness and g-T gconnectedness, respectively, are absolute properties of a g-T-set, a T g -set, and a g-T g -set [3,6,7,8,9,10,11]. Typical examples of g-T-connectedness in T -spaces are α, β, γ-connectedness [12,13,14]; examples of T g -connectedness in T g -spaces are semi * α, s, gb-connectedness [2,15,16], whereas examples of g-T g -connectedness in T g -spaces are bT µ , µ-rgb, π p-connectedness [17,18,19], among others.…”