The Lefschetz fixed point theory for morphisms in topological vector spaces

Abstract

The Lefschetz Fixed Point Theorem for compact absorbing contraction morphisms (${\mathbb{CAC}}$-morphisms) of retracts of open subsets in admissible spaces in the sense of Klee is proved. Moreover, the relative version of the Lefschetz Fixed Point Theorem and the Lefschetz Periodic Theorem are considered. Additionally, a full classification of morphisms with compact attractors in the non-metric case is obtained.