On strong and weak sets in topological spaces

Abstract

We explore the idea of sets in topological spaces that are usually named strong and weak sets. We start by providing definitions, examples and basic properties for the two types of sets. We compare these sets and their relations are introduced and studied. Also, we provide theorems and examples about these concepts in topological space and obtained a lot of characteristics and properties of such notions. A class of functions has been found in topological spaces which use strong and weak sets. In addition, strong and weak sets are independent, that cannot be equivalent under any condition.

Subject Classification:

• 54A05
• 54C05
• 54D99

Keywords:

• Minimal open sets
• Maximal closed sets
• Strong sets
• Weak sets
• Topological spaces