Mathematical modeling of finite topologies

Keywords: finite topology, mathematical modeling
Published online: 2020-12-29

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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How to Cite
(1)
MonabbatiS., TorabiH. Mathematical Modeling of Finite Topologies. Carpathian Math. Publ. 2020, 12 (2), 434-442.