More on Tie-points and homeomorphism in N^*
Logic
2007-11-21 v1 General Topology
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 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^* .
Cite
@article{arxiv.0711.3038,
title = {More on Tie-points and homeomorphism in N^*},
author = {Alan Dow and Saharon Shelah},
journal= {arXiv preprint arXiv:0711.3038},
year = {2007}
}