On Suitable Sets in a Top-Group

Abstract

Many researchers for their importance and their useful applications had studied the suitable sets. This study presents full description of these sets with a number of topological concepts. A suitable set is presented as a special type with the conditions for some of the topological concepts. In addition, a special subset of the topological G has been described in two different ways to achieve the same goal. The first one is based on several concepts, such as the closure of subset, discrete topology and closed of the set of the identity element, whereas, the second way is based on two concepts, such as the locally compact and the separation axioms. It is, however, important to note that some of the topological groups have suitable sets, while, others do not.