The Katowice problem and autohomeomorphisms of ω0⁎

David Chodounský, Alan Dow, Klaas Pieter Hart, Harm de Vries

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)


We show that the existence of a homeomorphism between ω0⁎ and ω1⁎ entails the existence of a non-trivial autohomeomorphism of ω0⁎. This answers Problem 441 in [8]. We also discuss the joint consistency of various consequences of ω0⁎ and ω1⁎ being homeomorphic.
Original languageEnglish
Pages (from-to)230-237
Number of pages8
JournalTopology and Its Applications: a journal devoted to general, geometric, set-theoretic and algebraic topology
Publication statusPublished - 2016


  • Katowice problem
  • Homeomorphism
  • Non-trivial autohomeomorphism
  • Čech–Stone remainder
  • ω0⁎
  • ω1⁎
  • Isomorphism
  • Non-trivial automorphism
  • Quotient algebra
  • P(ω0)/fin
  • P(ω1)/fin


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