Semihomeomorphisms

On Ω-closed sets and Ωs-closed sets in topological spaces

“…A function f : X → Y is said to be semi-closed [15] (resp. pre-semi-closed [16]) if for each closed (resp. semi-closed) set F of X, f (F ) is semi-closed in Y .…”

Some Properties of θ-Semigeneralized Pre Continuous Functions

“…(vii) θ-gs-closed [19] [20], α-continuous [16], gspcontinuous [8], gp-continuous [3], gpr-continuous [10], θ-g-continuous [9], αgscontinuous [24], sgp-continuous [17], θ-sg-continuous [6], θ-gs-continuous [18]) if f -1 (V) is semi-closed(resp. pg-closed, α-closed, gsp-closed, gp-closed, gpr-closed, θ-g-closed, αgs-closed, sgp-closed, θ-sg-closed, θ-gs-closed) in X for every closed set V of Y.…”

“…In 1963, Levine [12] studied the weak forms of continuity called semicontinuity. Mashhour et al [15,16], Rajamani et al [24] have introduced pre-continuity, α-continuity and αgs-continuity respectively, which are weaker forms of continuous functions.…”

Functions and regularity of topological spaces

“…A function f is called α-cl osed [14] (resp. pr e-α-cl osed [5]; semi -cl osed [17]; pr e-semi -cl osed [26]), if f (U ) is an α-closed (resp. an α-closed; a semiclosed; a semi-closed) subset of (Y , σ) for each closed (resp.…”