This article is cited in 2 papers

Research articles

Method for constructing one-point expansions of a topology on a finite set and its applications

V. I. Arnautov^a, A. V. Kochina

^a Institute of Mathematics and Computer Science, Academy of Sciences of Moldova

Abstract: The article consists of two parts. In the first part we present an algorithm which allows to receive, for any topology $\tau$ which is given on a set $X $ from $n$ elements, all topologies on the set $X\bigcup\{y\}$ each of which induces the topology $\tau$ on the set $X $. In the second part (as an example) this algorithm is applied for calculation of the number of topologies on the set $Y$ each of which induces the discrete topology on the set $X$.

Keywords and phrases: finite set, topologies, one-point expansions, lattice isomorphic.

MSC: 54A10

Received: 16.09.2010

Language: English

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