Given uniformly homeomorphic metric spaces $$X$$ and $$Y$$ , it is proven that hyperspaces $$C(X)$$ $$C(Y)$$ are homeomorphic, where denotes the collection of all nonempty closed subsets endowed with Hausdorff distance. Gerald Beer has proved hyperspace an Atsuji space when either compact or discrete. An a generalization as well discrete spaces. In this paper, we investigate space, class subspa...

Abstract. According to Thurston’s classification, the set of homotopy classes orientation-preserving homeomorphisms orientable surfaces is split into four disjoint subsets. A class from each subset characterized by existence a homeomorphism called canonical form, namely: periodic homeomorphism, reducible nonperiodic algebraically finite order, that not an and pseudo-Anosov homeomorphism. forms ...

This paper is concerned with homeomorphisms of Euclidean spaces onto themselves, with bounded orbits. The following results are obtained. (1) A homeomorphism of E onto itself has both bounded orbits and an equicontinuous family of iterates iff it is a conjugate of either a rotation or a reflection; (2) An example of Bing is modified to produce a fixed point free, orientation preserving homeomor...

In this paper a new class of homeomorphism called minimal Regular weakly and maximal are introduced investigated during process some properties the concepts have been studied.

The homeomorphism problem is, given two compact n-manifolds, is there an algorithm to decide if the manifolds are homeomorphic or not. The homeomorphism problem has been solved for many important classes of 3-manifolds especially those with embedded 2-sided incompressible surfaces (cf [12], [15],[16]), which are called Haken manifolds. It is also well-known that the homeomorphism problem is eas...

We derive a homeomorphism invariant for those tiling spaces which are made by rather general substitution rules on polygonal tiles, including those tilings, like the pinwheel, which contain tiles in infinitely many orientations. The invariant is a quotient of Čech cohomology, is easily computed directly from the substitution rule, and distinguishes many examples, including most pinwheel-like ti...

We shall show that for a given homeomorphism type and a set of end invariants (including the parabolic locus) with necessary topological conditions which a topologically tame Kleinian group with that homeomorphism type must satisfy, there is a limit of minimally parabolic, geometrically finite Kleinian groups having exactly that homeomorphism type and end invariants. This shows that the Bers-Th...