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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

  • Read count 16
  • Date of publication 10-07-2025
  • Main LanguageIngliz
  • Pages32-35
English

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

№ Author name position Name of organisation
1 Sabrbaeva E.K. student Mathematics of Karakalpak State University
№ Name of reference
1 1.LLESHI POLLOZHANI, F., RASIMI, K., SADIKI, F., & BEXHETI, B. (2022). METRIZABILITY OF TOPOLOGICAL SPACES. Journal of Natural Sciences and Mathematics of UT, 7(13-14), 114-120.2.Shravan, K., Tripathy, B. C., & Pandu, M. (2021). Metrizability of multiset topological spaces. SERIES III-MATEMATICS, INFORMATICS, PHYSICS, 13(2), 683-696.3.Когаловский, С. Р. (2022). О ПРОПЕДЕВТИКЕ КУРСА ТОПОЛОГИИ. InСовременные проблемы и перспективы обучения математике, физике, информатике в школе и вузе (pp. 27-30).4.Савельев, В. М. (2019). ОСОБЕННОСТИ ОБУЧЕНИЯТОПОЛОГИИ ДЛЯ ПОВЫШЕНИЯ КОМПЕТЕНТНОСТИ БУДУЩИХ УЧИТЕЛЕЙ МАТЕМАТИКИ. In Современный учитель дисциплин естественнонаучного цикла (pp. 81-83).5.Юнусов, Г. Г., & Болтаев, Х. Х. (2024). Описание и категорные свойства функтора полуаддитивных функционалов. Монография.-Tашкент:«NIF MSH», 2024.–87 стр.
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