Eurasian Journal of Mathematical Theory and Computer Sciences 5-jild 6-son (2025) · 32–35-betlar

METRIZABILITY OF TOPOLOGICAL SPACES AND THEIR COMPACT PROPERTIES

Sabırbaeva, Elmira

DOI: 10.5281/zenodo.15730872 · Manbada o'qish → · PDF (manba serverida)

Annotatsiya

This article discusses the conditions under which a topological space is metrizable and how this relates to compactness. Key metrization theorems, such as those by Urysohn and Nagata-Smirnov, are examined. The article also explores the role of compactness in metrizable spaces, supported by examples like the Sorgenfrey line and Cantor set. Applications in analysis, computer science, and control theory demonstrate the practical importance of these concepts.

Metrizability, compactness, topology, metric space, Urysohn theorem, Cantor set, product topology, functional analysis.

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