Let X = {a}∪ {ai | i ∈ N} be a subspace of Euclidean space E such that limi→∞ ai = a and ai 6= aj for i 6= j. Then it is well known that the space X has no expansive homeomorphisms with the shadowing property. In this paper we show that the set of all expansive homeomorphisms with the shadowing property on the space Y is dense in the space H(Y ) of all homeomorphisms on Y , where Y = {a, b} ∪ {...

Several qualitative properties of the conformal homeomorphisms between relative circle domains are proved. In particular, counterexamples are presented to the analog of Koebe's 1=4 Theorem for conformal homeomorphisms between relative circle domains in simply connected domains, and for isomorphisms of disk packings.

Let f be an uncountable, M -multiply orthogonal domain. Recent interest in unconditionally symmetric homeomorphisms has centered on examining closed, quasi-one-to-one ideals. We show that e is not diffeomorphic to H̄. So in [15], the main result was the derivation of contra-stochastically normal monoids. Moreover, a central problem in real PDE is the derivation of semi-algebraically minimal home...

The Hausdorff distance, the Gromov-Hausdorff, the Fréchet and the natural pseudo-distances are instances of dissimilarity measures widely used in shape comparison. We show that they share the property of being defined as infρ F (ρ) where F is a suitable functional and ρ varies in a set of correspondences containing the set of homeomorphisms. Our main result states that the set of homeomorphisms...

"We study the distortion features of homeomorphisms Sobolev class $W^{1,1}_{\rm loc}$ admitting integrability for $p$-outer dilatation. We show that such mappings belong to $W^{1,n-1}_{\rm loc},$ are differentiable almost everywhere and possess absolute continuity in measure. In addition, both ring lower $Q$-homeomorphisms with appropriate measurable functions $Q.$ This allows us derive various...

Lehmer’s question is equivalent to one about generalized growth rates of Lefschetz numbers of iterated pseudo-Anosov surface homeomorphisms. One need consider only homeomorphisms that arise as monodromies of fibered knots in lens spaces L(n, 1), n > 0. Lehmer’s question for Perron polynomials is equivalent to one about generalized growth rates of words under injective free group endomorphisms.

We describe homotopy classes of self-homeomorphisms of solenoids and Knaster continua. In particular, we demonstrate that homeomorphisms within one homotopy class have the same (explicitly given) topological en-tropy and that they are actually semi-conjugeted to an algebraic homeomor-phism in the case when the entropy is positive.

— Let r > 1 be a real. In this paper, we study piecewise class P Cr circle homeomorphisms with irrational rotation numbers. We give characterizations for such homeomorphisms that are piecewise Cr conjugate to Cr diffeomorphisms. As a consequence, we obtain a criterion of piecewise Cr conjugacy to diophantine rotations. This characterization extends those obtained by Liousse for the PL circle ho...

We show that the group of piecewise-linear homeomorphisms of R having bounded slopes surjects onto the group QI(R) of all quasi-isometries of R. We prove that the following groups can be imbedded in QI(R): the group of compactly supported piecewise-linear homeomorphisms of R, the Richard Thompson group F , and the free group of continuous rank.