HAQIQIY SONLAR TO‘PLAMIDA ZARISKIY VA METRIK TOPOLOGIYALARDA OCHIQ VA YOPIQ TO‘PLAMLAR VA UNIVERSAL FAZO

Abstract

This paper provides a comparative analysis of the concepts of open and closed sets in Zariski and metric topologies defined on the set of real numbers ℝ. The study examines the foundational principles of these two topologies, their interpretation through open and closed sets, and their theoretical differences. It is shown that in metric topology, open sets are defined based on the notion of distance and possess an intuitive structure.