Good coverings of proximal Alexandrov spaces. Path cycles in the extension of the Mitsuishi-Yamaguchi good covering and Jordan Curve Theorems

Peters J. F., Vergili T.

APPLIED GENERAL TOPOLOGY, cilt.24, sa.1, ss.25-45, 2023 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.4995/agt.2023.17046
  • Dergi Adı: APPLIED GENERAL TOPOLOGY
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals, DIALNET
  • Sayfa Sayıları: ss.25-45
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

This paper introduces proximal path cycles, which lead to the main results in this paper, namely, extensions of the Mitsuishi-Yamaguchi Good Coverning Theorem with different forms of Tanaka good cover of an Alexandrov space equipped with a proximity relation as well as extension of the Jordan curve theorem. In this work, a path cycle is a sequence of maps h1,...,hi,...,hn-1 mod n in which hi  : [ 0,1 ] → X and hi(1) = hi+1(0) provide the structure of a path-connected cycle that has no end path. An application of these results is also given for the persistence of proximal video frame shapes that appear in path cycles.