Good coverings of proximal Alexandrov spaces. Path cycles in the extension of the Mitsuishi-Yamaguchi good covering and Jordan Curve Theorems
APPLIED GENERAL TOPOLOGY, cilt.24, sa.1, ss.25-45, 2023 (ESCI, Scopus)
- 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.