# Sh:917

- Dow, A. S., & Shelah, S. (2009).
*More on tie-points and homeomorphism in \mathbb N^\ast*. Fund. Math.,**203**(3), 191–210. arXiv: 0711.3038 DOI: 10.4064/fm203-3-1 MR: 2506596 -
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} }