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 ...

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.

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.

The Lefschetz fixed point theorem provides a powerful obstruction to the existence of minimal homeomorphisms on well-behaved spaces such as finite CW-complexes. We show that these obstructions do not hold for more general spaces. Minimal are constructed compact connected metric with any prescribed finitely generated $K$-theory or cohomology. In particular, although non-zero Euler characteristic...

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

Let K be a closed subset of a smooth manifold M, and let f : K ! K be a continuous self-map of K. We say that f is smoothable if it is conjugate to the restriction of a smooth map by a homeomorphism of the ambient space M. We give a necessary condition for the smoothability of the faithfully innnitely interval-renormalizable homeomorphisms of Cantor sets in the unit interval. This class contain...

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...

We initiate a study of homeomorphisms f with constant principal strains (cps) between smoothly bounded planar domains D, D′. An initial result shows that in order for there to be such a mapping of a given Jordan domainD ontoD′, a certain condition of an isoperimetric nature must be satisfied by the latter. Thereafter, we establish the fundamental fact that principal strain lines (characteristic...