Abstract
Zero sets and their role in topology Sara Ibrahim Hassan Altawiry University of Tripoli (2022) Supervisor: Prof.Mabruk Ali Sola Abstract If X is a Tychonoff space a subset Z of X is called a zero set if Z=f ⃖({0}) = { x : f(x)=0} for some continuous real- valued function f. Zero sets were exploited in systematic way in the study of C(X), and to study the relation between topological properties of the space X and algebraic properties of the ring C(X). The aim of this paper is to study basic properties of zero sets, Z-filters and to use them to characterize the maximal ideals of the ring of continuous functions C(X).