A homeomorphism f : X → X of a compactum X is expansive (resp. continuum-wise expansive) if there is c > 0 such that if x, y ∈ X and x 6= y (resp. if A is a nondegenerate subcontinuum of X), then there is n ∈ Z such that d(f(x), f(y)) > c (resp. diam f(A) > c). We prove the following theorem: If f is a continuum-wise expansive homeomorphism of a compactum X and the covering dimension of X is po...

In this paper, some fixed point theorems for nonexpansive mappings in partially ordered spherically complete ultrametric spaces are proved. In addition, we investigate the existence of fixed points for nonexpansive mappings in partially ordered non-Archimedean normed spaces. Finally, we give some examples to discuss the assumptions and support our results.

We study expansive dynamical systems in the setting of distributive lattices and their automorphisms, usual notion expansiveness for a homeomorphism compact metric space being particular case when lattice is topology phase ordered by inclusion automorphism one induced homeomorphism, mapping open sets to sets. prove this context generalizations Mañé's Theorem Utz's about finite dimensionality an...

In this work we introduce a concept of expansiveness for actions connected Lie groups. We study some its properties and investigate implications expansiveness. the centralizer expansive CW-expansiveness pseudo-group actions. As an application, prove positiveness geometric entropy foliations group