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Random Topologies on Finite Sets and Their Threshold Functions

Maclean, Catriona; O'Connell, Neil


Keyword(s): random topologies; random functions; power sets

Abstract: For each integer n, there is a natural family of probability distributions on the set of topologies on a set of n elements, parameterised by an integer variable, m. We will describe how these are constructed and analysed, and find threshold functions (for m in terms of n) for various topological properties.

23 Pages

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