A note on θ‐generalized closed sets

C W Baker

doi:10.1155/s0161171201003945

Abstract

The purpose of this note is to strengthen several results in the literature concerning the preservation of θ‐generalized closed sets. Also conditions are established under which images and inverse images of arbitrary sets are θ‐generalized closed. In this process several new weak forms of continuous functions and closed functions are developed.

Highlights

Dontchev and Maki [5] have introduced the concept of a θ-generalized closed set
The purpose of this note is to strengthen slightly some of the results in [5] concerning the preservation of θ-generalized closed sets. This is done by using the notion of a θ-c-closed set developed by Baker [2]. These sets turn out to be a very natural tool to use in investigating the preservation of θ-generalized closed sets
In this process we introduce a new weak form of a continuous function and a new weak form of a closed function, called θ-g-c-continuous and θ-g-c-closed, respectively

Summary

Introduction

Dontchev and Maki [5] have introduced the concept of a θ-generalized closed set. A set A is said to be θ-open provided that A = Intθ(A). A set A is said to be θ-generalized closed (or briefly θ-g-closed) provided that Clθ(A) ⊆ U whenever A ⊆ U and U is open. A function f : X → Y is said to be θ-gclosed provided that f (A) is θ-g-closed in Y for every closed subset F of X.

Results

Conclusion