Tie-points and fixed-points in $\mathbb N^*$

by Dow and Shelah. [DwSh:916]
Topology and its Applications, 2008
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 N setminus N (e.g. [veli.oca, ShSt735]) and in the recent study of (precisely) 2-to-1 maps on beta N setminus N . In these cases the tie-points have been the unique fixed point of an involution on beta N setminus N . This paper is motivated by the search for 2-to-1 maps and obtaining tie-points of strikingly differing characteristics.

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