Tie-points and fixed-points in N^*

2007/11/19 by Alan Dow, Saharon Shelah, Dow, Alan +1 · 3 citations
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras #math.GN #math.LO

paper · pdf · doi:10.48550/arxiv.0711.3037

published as Topology Appl. 155 No. 15 (2008) 1661--1671

arxiv created 2007/11/19 · openalex publication_date 2007/11/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A point x is a (bow) tie-point of a space X if X setminus x can be partitioned into (relatively) clopen sets each with x in its closure. Tie-points have appeared in the construction of non-trivial autohomeomorphisms of betaN setminus N and in the recent study of (precisely) 2-to-1 maps on betaN setminus N . In these cases the tie-points have been the unique fixed point of an involution on betaN setminus N. This paper is motivated by the search for 2-to-1 maps and obtaining tie-points of strikingly differing characteristics.

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