Digital Lusternik-Schnirelmann category of digital functions

Year 2020, Volume: 49 Issue: 4, 1414 - 1422, 06.08.2020

Tane Vergili , Ayse Borat

https://doi.org/10.15672/hujms.559796

Cited By: 3

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.

Keywords

Lusternik-Schnirelmann category, Digital topology, digital LS category

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