In this paper we study the classification of self-homeomorphisms of closed, connected, oriented 4-manifolds with infinite cyclic fundamental group up to pseudoisotopy, or equivalently up to homotopy. We find that for manifolds with even intersection form homeomorphisms are classified up to pseudoisotopy by their action on π1, π2 and the set of spin structures on the manifold. For manifolds with...

We say that a space X has the separation property provided that if A and B are subsets of X with A countable and B first category, then there is a homeomorphism f : X → X such that f(A) ∩ B = ∅. We prove that a Borel space with this property is Polish. Our main result is that if the homeomorphisms needed in the separation property for the space X come from the homeomorphisms given by an action ...

In this paper, we give an overview of some topics involving behavior of homeomorphisms and ways in which real analysis can arise in geometric settings.

We generalize the model theory of small profinite structures developed by Newelski to the case of compact metric spaces considered together with compact groups of homeomorphisms.

Let F = η be arbitrary. In [5], the main result was the derivation of homeomorphisms. We show that

We continue to study topological properties of the group Homeo(X) of all homeomorphisms of a Cantor set X with respect to the uniform topology τ , which was started in [B-K 1], [B-D-K 1; 2], [B-D-M], and [M]. We prove that the set of periodic homeomorphisms is τ -dense in Homeo(X) and deduce from this result that the topological group (Homeo(X), τ) has the Rokhlin property, i.e., there exists a...

In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodic shadowing and the average shadowing property also have the shadowing property and then are chao...