Zero sets and their role in topology




Master Thesis

Thesis title

جامعة طرابلس


Sarah Ibrahim hassn


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).

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