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IMCS/Publications/BASM/Issues/BASM n.2 (69), 2012/

Method of construction of topologies on any finite set

Authors: Arnautov Vladimir
Keywords: finite set, topologies, lattice of all open sets, atoms, quasiatoms.

Abstract

Let a topology τ be defined on a finite set. We give the definition of quasiatoms in the lattice (τ, ⊆) and study their properties. For any splitting of a finite set X into k subsets we give a method of constructing any topology on the set X for which this splitting is the set of all quasiatoms and the weight of this topological space is equal to k.

Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
5 Academiei str. Chişinău MD-2028, Moldova
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