METRIZABILITY OF TOPOLOGICAL SPACES AND THEIR COMPACT PROPERTIES

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.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-06-24
DOI
https://doi.org/10.5281/zenodo.15730871
Primary Topic
Orthopaedic implants and arthroplasty
Type
article
Field-Weighted Citation Impact
0.00
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article

METRIZABILITY OF TOPOLOGICAL SPACES AND THEIR COMPACT PROPERTIES

Zenodo (CERN European Organization for Nuclear Research)
Orthopaedic implants and arthroplasty
article

METRIZABILITY OF TOPOLOGICAL SPACES AND THEIR COMPACT PROPERTIES

article en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 36%
Orthopaedic implants and arthroplasty
DOIOpen Access PDFOpenAlex
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METRIZABILITY OF TOPOLOGICAL SPACES AND THEIR COMPACT PROPERTIES · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS