On topological properties of families of finite sets

Claribet Piña, Carlos Uzcátegui

Published 2011-04-20, updated 2015-11-23Version 2

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.