Method of construction of topologies on any finite set

V. I. Arnautov

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova

Abstract: Let a topology $\tau$ be defined on a finite set. We give the definition of quasiatoms in the lattice $(\tau,\subseteq)$ 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 $k$.

Keywords and phrases: finite set, topologies, lattice of all open sets, atoms, quasiatoms.

MSC: 54A10

Received: 24.05.2012
Revised: 21.09.2012

Language: English

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