# Sh:916

• Dow, A. S., & Shelah, S. (2008). Tie-points and fixed-points in \mathbb N^*. Topology Appl., 155(15), 1661–1671.
• 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 \beta{\mathbb N} \setminus {\mathbb N} (e.g. [veli.oca, ShSt735]) and in the recent study of (precisely) 2-to-1 maps on \beta{\mathbb N} \setminus {\mathbb N}. In these cases the tie-points have been the unique fixed point of an involution on \beta{\mathbb N} \setminus {\mathbb N}. This paper is motivated by the search for 2-to-1 maps and obtaining tie-points of strikingly differing characteristics.
• Version 2007-08-12_11 (19p) published version (11p)
Bib entry
@article{Sh:916,
author = {Dow, Alan Stewart and Shelah, Saharon},
title = {{Tie-points and fixed-points in $\mathbb N^*$}},
journal = {Topology Appl.},
fjournal = {Topology and its Applications},
volume = {155},
number = {15},
year = {2008},
pages = {1661--1671},
issn = {0166-8641},
mrnumber = {2437015},
mrclass = {03E35 (54H25)},
doi = {10.1016/j.topol.2008.05.002},
note = {\href{https://arxiv.org/abs/0711.3037}{arXiv: 0711.3037}},
arxiv_number = {0711.3037}
}