Abstract

CUEVAS ROZO, Julian L.  and  SARRIA ZAPATA, Humberto. Computation of matrices and submodular functions values associated to finite topological spaces. Rev. acad. colomb. cienc. exact. fis. nat. [online]. 2017, vol.41, n.158, pp.127-136. ISSN 0370-3908.  https://doi.org/10.18257/raccefyn.409.

The submodular functions have shown their importance in the study and characterization of multiple properties of finite topological spaces, from numeric values provided by such functions (Sarria, Roa & Varela, 2014). However, the calculation of these values has been performed manually or even using Hasse diagrams, which is not practical. In this article, we present some algorithms that let us calculate some kind of polymatroid functions, specifically fU , fD , and rA , which define a topology, by using topogenous matrices.

Keywords : Finite topological spaces; submodular functions; topogenous matrix; Stong matrix..

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