Presemiclosed mappings

Abstract

The purpose of this paper is to investigate the prope~ies ofpresemlclosed mappings and improve some already established results. Moreover, it is shown that, if the domain space is To, then optimal continuity and homeomorphism coincide (Theorem 4.18).A M S (MOS) subject classification (1980). Primary 54C10.

Optimality of mappings and some separation axioms

“…Moreover, they have observed [19,Remark 4.16] that presemi-closed in that result cannot be replaced by semi-closed.…”

“…If (X, τ) is T 1 then (Y, σ) is so.Proof Quite similar to the proof of Theorem 30.Compare Theorem 31 with[19, Theorem 4.18].Theorem 32 Let f : (X, τ) → (Y, σ) be optimally irresolute and (X, τ) be semi-T 1 . Then f is a semi-homeomorphism.…”

“…Garg and Sivaraj showed [19,Theorem 4.8] that if a surjection f : (X, τ) → (Y, σ) is continuous, semi-open, and pre-semi-closed, and if (X, τ) is s-regular, then so is (Y, σ). Moreover, they have observed [19,Remark 4.16] that presemi-closed in that result cannot be replaced by semi-closed.…”

On quasi $${\mathcal{H}}$$ -closed subspaces

“…Other properties obtained later and concerning quasi H-closedness (briefly: Q.H.C.) are scattered in the literature-see for instance [4,13,15,17]. The purpose of the present paper is to obtain some further properties of sets Q.…”