With each isolating block for a homeomorphism of an orientable manifold we associate a cup product pairing. Up to an isomorphism, this is a pairing of the discrete Conley indices of the homeomorphism and its inverse on the isolating block. We show that this pairing is nondegenerate. As a corollary we prove a time duality result for the discrete Conley index. 0. Introduction The observation that...

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 paper we introduce a new class of closed maps namely g#s-closed also homeomorphisms called g#s*-homeomorphisms and prove that the set all form group under operation composition maps.