Digital Hurewicz theorem and digital homology theory

Author(s)

Samira Sahar Jamil, University of Karachi
Danish Ali, Institute of Business Administration, KarachiFollow

Author Affiliation

Danish Ali is Assistant Professor, Program Coordinator PhD/MS Mathematics & BS (Eco. & Maths.) and Mathematics & Astronomy Club at Institute of Business Administration (IBA), Karachi

Faculty / School

Faculty of Computer Sciences (FCS)

Department

Department of Mathematical Sciences

Was this content written or created while at IBA?

Yes

Document Type

Article

Source Publication

Turkish Journal of Mathematics

ISSN

1300-0098

Keywords

Cubical singular homology for digital images, Digital excision, Digital homology theory, Digital Hurewicz theorem, Digital topology

Disciplines

Mathematics

Abstract

In this paper, we develop homology groups for digital images based on cubical singular homology theory for topological spaces. Using this homology, we obtain two main results that make this homology different from alreadyexisting homologies of digital images. We prove digital analog of Hurewicz theorem for digital cubical singular homology. We also show that the homology functors developed in this paper satisfy properties that resemble the Eilenberg-Steenrod axioms of homology theory, in particular, the homotopy and the excision axioms. We finally define axioms of digital homology theory.

Indexing Information

HJRS - X Category, Scopus, Web of Science - Science Citation Index Expanded (SCI)

Recommended Citation

Jamil, S. S., & Ali, D. (2020). Digital Hurewicz theorem and digital homology theory. Turkish Journal of Mathematics, 44 (3), 739-759. Retrieved from https://ir.iba.edu.pk/faculty-research-articles/164

Publication Status

Published