Topologies on $Z^{n}$ that Are not Homeomorphic to the N-Dimensional Khalimsky Topological Space

Authors: Sang-Eon Han, Saeid Jafari, Jeong Min Kang

The present paper deals with two types of topologies on the set of integers, Z: a quasi-discrete topology and a topology satisfying the T½ -separation axiom. Furthermore, for each $n \in N$, we develop countably many topologies on Zn which are not homeomorphic to the typical n-dimensional Khalimsky topological space. Based on these different types of new topological structures on $Z^{n}$, many new mathematical approaches can be done in the fields of pure and applied sciences, such as fixed point theory, rough set theory, and so on.

Comments: 12 Pages.

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[v1] 2020-01-06 16:24:27

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