Digital Lusternik-Schnirelmann category of digital functions

VERGİLİ T., Borat A.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.49, no.4, pp.1414-1422, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.15672/hujms.559796
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1414-1422
  • Keywords: Lusternik Schnirelmann category, digital topology, TOPOLOGICAL COMPLEXITY
  • Karadeniz Technical University Affiliated: Yes

Abstract

Roughly speaking, the digital Lusternik-Schnirelmann category of digital images studies how far a digital image is away from being digitally contractible. The digital Lusternik-Schnirelmann category (digital LS category, for short) is defined in [A. Borat and T. Vergili, Digital Lusternik-Schnirelmann category, Turkish J. Math. 2018]. In this paper, we introduce the digital LS category of digital functions. We will give some basic properties and discuss how this new concept will behave if we change the adjacency relation in the domain and in the image of the digital function and discuss its relation with the digital LS category of a digital image.