A STUDY OF SOME PROPERTIES FOR CELLULAR-LINDELOF TOPOLOGICAL SPACES

Abstract

Based on Bella and Spadaro (2017), a topological space T is called cellular-Lindelof if for every family F of pairwise disjoint nonempty open subsets of T, there exists a Lindelof subspace L subset T such that F intersection L ≠ empty set for every F∈F. The aim of this paper is to investigate the properties of cellular Lindelof spaces, its relation with other spaces and find cardinal inequality for cellular-Lindelof spaces based on the Erdos and Rado theorem. The concept of cellular-Lindelof was utilized to show the properties of cellular-Lindelof spaces and its relation with other spaces. We obtain few examples of topological spaces which are not cellular-Lindelof. Erdos and Rado theorem is a theorem based on intersecting set families. Cardinal inequality that was found is based on lemma from Erdos and Rado theorem and information obtained from some journal papers. The study of cellular-Lindelof spaces is the extension study of Lindelof spaces and this is important as it can become a reference material for the future researchers. The central object of the study of topological dynamics is a topological dynamical system, where topological spaces needed. Thus, the study of cellular-Lindelof spaces is also important to the field of dynamical system.