@article{Han2022, 
author = {Sang-Eon Han},
title = {Semi-topological properties of the Marcus-Wyse topological spaces},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {7},
pages = {12742-12759},
keywords = {semi-open, semi-closed, semi-T3-space, Alexandroff space, semi-regular, semi-T1-space, regular open, Marcus-Wyse topology},
url = {https://www.sciopen.com/article/10.3934/math.2022705},
doi = {10.3934/math.2022705},
abstract = {Since the Marcus-Wyse (   M  W-, for brevity) topological spaces play important roles in the fields of pure and applied topology (see Remark 2.2), the paper initially proves that the    M  W-topological space satisfies the semi-       T    3  -separation axiom. To do this work more efficiently, we first propose several techniques discriminating between the semi-openness or the semi-closedness of a set in the    M  W-topological space. Using this approach, we suggest the condition for simple    M  W-paths to be semi-closed, which confirms that while every    M  W-path    P with    |    P    |  ≥  2 is semi-open, it may not be semi-closed. Besides, for each point    p  ∈                    Z              2   the smallest open neighborhood of the point    p is proved to be a regular open set so that it is semi-closed. Note that the    M  W-topological space is proved to satisfy the semi-       T    3  -separation axiom, i.e., it is proved to be a semi-       T    3  -space so that we can confirm that it also satisfies an    s-       T    3  -separation axiom. Finally, we prove that the semi-       T    3  -separation axiom is a semi-topological property.}
}