# Sh:917

• Dow, A. S., & Shelah, S. (2009). More on tie-points and homeomorphism in \mathbb N^\ast. Fund. Math., 203(3), 191–210.
• 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}=\mathbb N^* and in the recent study of (precisely) 2-to-1 maps on \mathbb N^*. In these cases the tie-points have been the unique fixed point of an involution on \mathbb N^*. One application of the results in this paper is the consistency of there being a 2-to-1 continuous image of \mathbb N^* which is not a homeomorph of \mathbb N^*.
• Version 2007-08-12_11 (14p) published version (20p)
Bib entry
@article{Sh:917,
author = {Dow, Alan Stewart and Shelah, Saharon},
title = {{More on tie-points and homeomorphism in $\mathbb N^\ast$}},
journal = {Fund. Math.},
fjournal = {Fundamenta Mathematicae},
volume = {203},
number = {3},
year = {2009},
pages = {191--210},
issn = {0016-2736},
mrnumber = {2506596},
mrclass = {03E50 (54A25 54D35)},
doi = {10.4064/fm203-3-1},
note = {\href{https://arxiv.org/abs/0711.3038}{arXiv: 0711.3038}},
arxiv_number = {0711.3038}
}