@article{Lee2023, 
author = {Sik Lee and Sang-Eon Han},
title = {Semi-separation axioms associated with the Alexandroff compactification of the    M  W-topological plane},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {8},
pages = {4592-4610},
keywords = {Marcus-Wyse topology, semi-T3-space, Alexandroff compactification, infinite MW-sphere, semi-regular, hereditary property},
url = {https://www.sciopen.com/article/10.3934/era.2023235},
doi = {10.3934/era.2023235},
abstract = {The present paper aims to investigate some semi-separation axioms relating to the Alexandroff one point compactification (Alexandroff compactification, for short) of the digital plane with the Marcus-Wyse (   M  W-, for brevity) topology. The Alexandroff compactification of the    M  W-topological plane is called the infinite    M  W-topological sphere up to homeomorphism. We first prove that under the    M  W-topology on                      Z              2   the connectedness of    X  (  ⊂                    Z              2    ) with        X    ♯    ≥  2 implies the semi-openness of    X. Besides, for the infinite    M  W-topological sphere, we introduce a new condition for the hereditary property of the compactness of it. In addition, we investigate some conditions preserving the semi-openness or semi-closedness of a subset of the    M  W-topological plane in the process of an Alexandroff compactification. Finally, we prove that the infinite    M  W-topological sphere is a semi-regular space; thus, it is a semi-       T    3  -space because it is a semi-       T    1  -space. Hence we finally conclude that an Alexandroff compactification of the    M  W-topological plane preserves the semi-       T    3   separation axiom.}
}