A Lefschetz-Hopf theorem for the functions of compact iterations

作者：Cauty Robert^*

来源：Journal fur die Reine und Angewandte Mathematik, 2017, 729(729): 1-27.

DOI：10.1515/crelle-2014-0134

We prove that a self-map f : X -> X of a convex subset X of a linear metric space has a fixed point if some iterate f(n) of f is compact in the sense that f(n) (X) is contained in a compact subset of X. This result is a partial case of a more general fixed-point theorem saying that a self-map f : X -> X of an algebraic ANR X has a fixed point if it has non-zero Lefschetz number Lambda (f) and some iterate f(n) of f is compact. The class of algebraic ANRs was introduced and studied by the author in 2005. It contains all ANRs and all convex subsets of linear metric spaces (more generally, all metrizable equiconnected spaces).

• 出版日期2017-8