2025/05/07 by Will Brian, Brian, Will, Alan Dow +3 · 1 voice
Mathematics · #Advanced Topology and Set Theory #Mathematical Dynamics and Fractals #Homotopy and Cohomology in Algebraic Topology
paper · doi:10.1016/j.topol.2025.109539
openalex publication_date 2025/08/08 · openalex created_date 2025/08/15 · openalex updated_date 2026/07/28
Let M = N × [ 0 , 1 ] . The natural projection π : M → N , which sends ( n , x ) to n , induces a projection mapping π ⁎ : M ⁎ → N ⁎ ⁎ ⁎ ⁎ , where M ⁎ ⁎ and N ⁎ ⁎ denote the Čech-Stone remainders of M and N , respectively. We show that CH implies every autohomeomorphism of N ⁎ lifts through the natural projection to an autohomeomorphism of M ⁎ . That is, for every homeomorphism h : N ⁎ → N ⁎ there is a homeomorphism H : M ⁎ → M ⁎ such that π ⁎ ∘ H = h ∘ π ⁎ . This complements a recent result of the second author, who showed that this lifting property is not a consequence of ZFC . Combining this lifting theorem with a recent result of the first author, we also prove that CH implies there is an order-reversing autohomeomorphism of H ⁎ , the Čech-Stone remainder of the half line H = [ 0 , ∞ ) .