Finite Models of Topological Varieties of Two Dimensions by Means of Directed Graphs
DOI:
https://doi.org/10.70882/Abstract
In this paper, a generalization of the concept of beat point, developed by Barmak and Minian for posets, is developed in a reflective binary or digraph structure. Using the beat point concept, we find the nucleus of a finite topological space. The classifier space of a two-dimensional topological manifold is described, which is obtained as a simplicial complex associated with a reflective binary structure. Finally, some finite models for two-dimensional topological varieties are described by means of a digraph, and a way of calculating the first homotopic group of a reflective binary structure is presented.
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Copyright (c) 2026 Mohammed Abdul Hussein Ghafil, Wissam Abbas Hussein, Mohammed Abdul Hussein Ghafil, Mohammed Abdul Hussein Ghafil (Author)
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