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## Fundamenta Mathematicae

2009 | 203 | 3 | 191-210

## More on tie-points and homeomorphism in ℕ*

EN

### Abstrakty

EN
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*.

191-210

wydano
2009

### Twórcy

autor
• University of North Carolina at Charlotte, Charlotte, NC 28223, U.S.A.
autor
• Department of Mathematics, Rutgers University, Hill Center, Piscataway, NJ 08854-8019, U.S.A.
• Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel