Mathematical modeling of finite topologies

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DOI:

https://doi.org/10.15330/cmp.12.2.434-442

Keywords:

finite topology, mathematical modeling

Abstract

Integer programming is a tool for solving some combinatorial optimization problems. In this paper, we deal with combinatorial optimization problems on finite topologies. We use the binary representation of the sets to characterize finite topologies as the solutions of a Boolean quadratic system. This system is used as a basic model for formulating other types of topologies (e.g. door topology and $T_0$-topology) and some combinatorial optimization problems on finite topologies. As an example of the proposed model, we found that the smallest number $m(k)$ for which the topology exists on an $m(k)$-elements set containing exactly $k$ open sets, for $k = 8$ and $k = 15$ is $3$ and $5$, respectively.

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Published

2020-12-29

How to Cite

(1)
Monabbati, S.; Torabi, H. Mathematical Modeling of Finite Topologies: Array. Carpathian Math. Publ. 2020, 12, 434-442.

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Section

Scientific articles