A fixed point theorem for the pseudo-circle

作者：Boronski J P^*

来源：Topology and Its Applications, 2011, 158(6): 775-778.

DOI：10.1016/j.topol.2011.01.023

• Fixed point
• Pseudo-circle
• Pseudo-arc
• Circle-like continuum
• Nielsen class

Let f:C -> C be a self-map of the C. Suppose that C is embedded into an annulus A, so that it separates the two components of the boundary of A. Let F : A -> A be an extension of f to A (i.e. F vertical bar C = f). If F is of degree d then f has at least vertical bar d - 1 vertical bar fixed points. This result generalizes to all plane separating circle-like continua.

• 出版日期2011-4-1