2007/11/19 by Alan Dow, Saharon Shelah, Dow, Alan +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN) #Logic (math.LO) #math.GN #math.LO
paper · pdf · doi:10.48550/arxiv.0711.3038
published as Fund. Math. 203 No. 3 (2009) 191--210
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
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= N^* and in the recent study of (precisely) 2-to-1 maps on N^*. In these cases the tie-points have been the unique fixed point of an involution on N^*. One application of the results in this paper is the consistency of there being a 2-to-1 continuous image of N^* which is not a homeomorph of N^* .