Ozgur Ege

) In this article we study the digital cubical homology groups of digital images which are based on the cubical homology groups of topological spaces in algebraic topology. We investigate some fundamental properties of cubical homology groups of digital images. We also calculate cubical homology groups of certain 2-dimensional and 3-dimensional digital images. We give a relation between digital simplicial homology groups and digital cubical homology groups. Moreover we show that the Mayer-Vietoris Theorem need not be hold in digital images.

In this article we give characteristic properties of the simplicial homology groups of digital images which are based on the simplicial homology groups of topological spaces in algebraic topology. We then investigate Eilenberg-Steenrod axioms for the simplicial homology groups of digital images. We state universal coefficient theorem for digital images. We conclude that the Künneth formula for simplicial homology doesn't be hold in digital images. Moreover we show that the Hurewicz Theorem need not be hold in digital images. Copyright © AJCTA, all rights reserved.

In this paper, we introduce a digital H-space, a digital H-group and a digital H-map between digital H-spaces. We give definition of digital H-space and then its basic properties. We give an example which is a digital H-space. Some conclusions about digital H-spaces are associated with algebraic topology. Furthermore we obtained some results about digital H-spaces. At the end of, the importance of digital H-space in digital topology is discussed.

In this paper, our aim is to study the digital version of Steenrod Algebra. For this purpose, we define the digital cohomology operations and deal with main properties of digital Steenrod squares. Moreover, some related results are given for digital images. We finally explain the theory with nice examples.

In this paper we study some results related to the simplicial homology groups of 2D digital images. We show that if a bounded digital image Z X  is nonempty and  -connected, then its homology groups at the first dimension are a trivial group. In general, we prove that the homology groups of the operands of a wedge of digital images need not be additive.