More on tie-points and homeomorphism in ℕ*

Alan Dow, and Saharon Shelah. "More on tie-points and homeomorphism in ℕ*." Fundamenta Mathematicae 203.3 (2009): 191-210. <http://eudml.org/doc/286149>.

@article{AlanDow2009,
abstract = {A point x is a (bow) tie-point of a space X if X∖x can be partitioned into (relatively) clopen sets each with x in its closure. We denote this as $X = A \{⋈ \limits _\{x\}\} B$ where A, B are the closed sets which have a unique common accumulation point x. Tie-points have appeared in the construction of non-trivial autohomeomorphisms of βℕ = ℕ* (by Veličković and Shelah Steprans) and in the recent study (by Levy and Dow Techanie) 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*.},
author = {Alan Dow, Saharon Shelah},
journal = {Fundamenta Mathematicae},
keywords = {automorphism; Stone-Čech compactification; fixed points},
language = {eng},
number = {3},
pages = {191-210},
title = {More on tie-points and homeomorphism in ℕ*},
url = {http://eudml.org/doc/286149},
volume = {203},
year = {2009},
}

TY - JOUR
AU - Alan Dow
AU - Saharon Shelah
TI - More on tie-points and homeomorphism in ℕ*
JO - Fundamenta Mathematicae
PY - 2009
VL - 203
IS - 3
SP - 191
EP - 210
AB - A point x is a (bow) tie-point of a space X if X∖x can be partitioned into (relatively) clopen sets each with x in its closure. We denote this as $X = A {⋈ \limits _{x}} B$ where A, B are the closed sets which have a unique common accumulation point x. Tie-points have appeared in the construction of non-trivial autohomeomorphisms of βℕ = ℕ* (by Veličković and Shelah Steprans) and in the recent study (by Levy and Dow Techanie) 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*.
LA - eng
KW - automorphism; Stone-Čech compactification; fixed points
UR - http://eudml.org/doc/286149
ER -