CHAIN OF A SET IN A COVERING AND CHAIN COMPONENTS UP TO A COVERING

Emin DURMISHI, Zoran MISAJLESKI, Flamure SADIKU, Alit IBRAIMI

Abstract

A chain in the open covering of a topological space that joins and is a finite sequence of elements of such that is the first member, is the last member and every two consecutive members of the sequence have a nonempty intersection. By it is meant the union of all elements of the covering for which there are chains joining them with and is the set that consists of all sets for each A chain in that joins and is a finite sequence of elements of such that is contained in the first element of the sequence, is contained in the last element and every two consecutive elements of the sequence have a nonempty intersection. A -chain component of an element is the set that consists of all such that there exists a chain in that joins and . We prove that for any and any hence consists of -chain components. As a consequence, chain connectedness is characterized using the notion.

Pages: 365 - 368