# Sh:916

- Dow, A. S., & Shelah, S. (2008).
*Tie-points and fixed-points in \mathbb N^**. Topology Appl.,**155**(15), 1661–1671. arXiv: 0711.3037 DOI: 10.1016/j.topol.2008.05.002 MR: 2437015 -
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} }