Chain connected set in a space

Abstract

The paper gives a generalization of connectedness and chain connectedness of a space that is more general than a topological space and it consists of a set and a family of coverings of the set. In these spaces we define the notions of connected and chain connected sets, that are generalization of the notions with the same name in a topological spaces ([1]), and we study their properties. Also, the notions of a chain relation and a chain component in a space that are generalization of a chain relation and a chain component in a topological space ([1]), are defined and their properties are presented. Some new results for topological spaces are also provided.