T_3/4-spaces and the digital line
by
Julian Dontchev
University of Helsinki
Coauthors: Maximilian Ganster, Haruo Maki

In Digital Topology, several spaces that fail to be T₁ are important in the study of the geometric and topological properties of digital images. Although the digital line (the major building block of the digital n-space) is neither a T₁-space nor an R₀-space, it satisfies a couple of separation axioms which are a bit weaker than T₁ and R₀, that is, the digital line is both a T_\frac34-space (hence a semi-T₁-space) and a semi-R₀-space. This inclines to indicate that further knowledge of the behavior of topological spaces satisfying these two weak separation axioms (and some related ones) is required. This is indeed the intention of this talk.

Date received: July 30, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabl-09.