More on Tie-points and homeomorphism in N^*

Alan Dow; Saharon Shelah

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arXiv · 0711.3038

More on Tie-points and homeomorphism in N^*

Alan Dow·Saharon Shelah

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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^* .

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Alan Dow, Saharon Shelah. 2007-11-19. More on Tie-points and homeomorphism in N^*. https://arxiv.org/abs/0711.3038

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