1.1. The main results. Let T denote the unit circle and D the unit disc. Suppose that f : T → T is a homeomorphism. Let f̂ : D → D be a homeomorphism too. We say that f̂ extends f if f̂ and f agree on T. All mappings in this paper are sense preserving (see the remark at the end of introduction). Definition 1.1. We say that a homeomorphism f : T → T is K-quasisymmetric if there exists a K-quasiconf...

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.