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On topological properties of families of finite sets

Authors
Journal
Journal of Combinatorial Theory Series A
0097-3165
Publisher
Elsevier
Volume
119
Issue
5
Identifiers
DOI: 10.1016/j.jcta.2012.02.003
Keywords
  • Uniform Families
  • Cantor–Bendixson Derivative
  • Partition Of Topological Spaces
Disciplines
  • Linguistics
  • Mathematics

Abstract

Abstract 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 ω-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.

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