Ismet Karaca

The Classification of Digital Covering Spaces

In this paper we classify digital covering spaces using the conjugacy class corresponding to a digital covering space.

Lefschetz fixed point theorem for digital images

In this article we study the fixed point properties of digital images. Moreover, we prove the Lefschetz fixed point theorem for a digital image. We then give some examples about the fixed point property. We conclude that sphere-like digital images have the fixed point property.MSC:55N35, 68R10, 68U05, 68U10.

Nilpotence relations in the mod-p Steenrod algebra

Abstract In our paper we generalize some results proved by Monks (Bol. Mex. Mat. Soc. 37 (1992) 401–416) and find formulas for the nilpotence of P ( n ) for certain values of n.

Digital fixed points, approximate fixed points, and universal functions

A. Rosenfeld introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approximate fixed points of digitally continuous functions. Among these are several results concerning the relationship between universal functions and the approximate fixed point property (AFPP).

Unstable modules over the Steenrod algebra

Abstract In this paper we generalize some results of Jmoui and Peterson (J. Pure Appl. Algebra 97 (1994) 37–50) to an odd prime p . In particular, we give a characterization in terms of the action of the Steenrod algebra of those unstable modules which are concentrated in even degrees and admit an injective resolution of which at least the first three terms are reduced.