Compactness with "gem-set"

Abstract

This paper introduced a new compactness space called Gem-compact space , pointcompact space and Prefect-compact space under the idea of "Gem-Set" in topological spaces and study some of their properties and relations among them with basic compact space.

Types of local functions via soft sets

“…(2)// By theorem [11] we must prove every soft point ℱ is closed soft set in * (̃). Since is finite then ℱ is finite, so ℱ ∈̃ , and (ℱ ) * = Φ but * (ℱ ) = (ℱ ) ∪ (ℱ ) * =(ℱ ) ∪ Φ = (ℱ ), so we get that ℱ is * −closed soft set.…”

“…The idea of local function is defined and studied by [4] where there is a very large constellation of researchers who have studied this definition and associate it with ideal and provide a definition ideal topological space and study it closely. It was also a special case study of local function and the definition of the separation axioms and some properties in [12], also in [11] and the study of compact on this definition. The goal of this here is to the local function and defines three different types of the local function in soft ideal topological space.…”

On Soft Turning Points

“…In 2015 Aysequl and Goknur (10) introduced I_ regular, I_ normal and found a squire relations between them. The properties for instance, separation axioms and compactness to more details (11,12). Moreover, Kanal el at.…”