To define the concept of U-chain connected sets and U-chain separated sets within topological spaces and examine their properties.
Defined U-chain connectedness and U-chain separatedness for sets in topological spaces.
Studied the properties and relationships of these newly defined sets.
Introduced a framework for understanding U-chain connectivity in topological spaces.
Identified key characteristics that distinguish U-chain connected sets from other types of connected sets.
Abstract
For an open covering U in a topological space in this paper we define a U-chain connected set, and a pair of U-chain separated sets in the topological space and study its properties.