Fan-Gottesman Compactification and Scattered Spaces

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Elmalı C. S., Uğur T.

Applied Mathematics and Nonlinear Sciences, cilt.5, sa.1, ss.475-478, 2020 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 5 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.2478/amns.2020.1.00045
  • Dergi Adı: Applied Mathematics and Nonlinear Sciences
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Applied Science & Technology Source, Compendex, zbMATH, DIALNET
  • Sayfa Sayıları: ss.475-478
  • Anahtar Kelimeler: Fan-Gottesman compactification, Scattered spaces
  • Atatürk Üniversitesi Adresli: Evet

Özet

Compactification is the process or result of making a topological space into a compact space. An embedding of a topological space X as a dense subset of a compact space is called a compactification of X. There are a lot of compactification methods but we study with Fan- Gottesman compactification. A topological space X is said to be scattered if every non-empty subset S of X contains at least one point which is isolated in S. Compact scattered spaces are important for analysis and topology. In this paper, we investigate the relation between the Fan- Gottesman compactification of T-3 space and scattered spaces. We show under which conditions the Fan-Gottesman compactification X* is a scattered.