When Compact Sets are -Closed

Abstract

This paper is devoted to introduce new concepts so called K( c)-spaces several various theorems about these concepts are provided in addition, further properties are studied such as the relationships between those concepts and other types of K( c)-spaces are investigated.

على مسافات gKc

“…whenever F is g-closed (g-open) subset of Y. Also the g ** -continuous image of gcompact is g-compact [2] and every g-closed subset of g-compact space is gcompact [5]. The author in [2] introduced the following :Let f be a homeomorphism function from a space X into space Y, if M is g-compact set in X, then f(M) is also g-compact.…”

“…Also the g ** -continuous image of gcompact is g-compact [2] and every g-closed subset of g-compact space is gcompact [5]. The author in [2] introduced the following :Let f be a homeomorphism function from a space X into space Y, if M is g-compact set in X, then f(M) is also g-compact. And if f is a homeomorphism function from a space X into space Y, and M is g-closed set in X, then f (M) is also g-closed.…”

“…And The author in [6] introduced the following definition: A space X is said to be K 2 space if ) A ( cl is compact, whenever A is compact set in X. Finally The author in [2] introduced the following definitions: A space X is said to be K(gc)or(gK (gc)) -space if every compact or(g-compact) set in X is gclosed.…”

“…It is known that compact subset of Hausdorff space is closed, this motivates the author [1] to introduce the concept of KC-spaces, and these are the spaces in which every compact subset is closed. In 2011 the authors [2] introduce new concepts namely K(gc) and gK(gc)-spaces. The aim of this paper is to continue the study KC-spaces.…”