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On topological properties of families of finite sets

By Claribet Piña and Carlos Uzcátegui


We present results about the Cantor-Bendixson index of some subspaces of a uniform family F of finite subsets of natural numbers with respect to the lexicographic order topology. As a corollary of our results we get that for any omega-uniform family F the restriction F|M is homeomorphic to F iff M contains intervals of arbitrary length of consecutive integers. We show the connection of these results with a topological partition problem of uniform families

Topics: Mathematics - Combinatorics, Primary 03E02, Secondary 05D10
Year: 2015
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