Related papers: Intrinsic isometries in Euclidean space

We investigate a relations of almost isometric embedding and almost isometry between metric spaces and prove that with respect to these relations: (1) There is a countable universal metric space. (2) There may exist fewer than continuum…

For a finite lattice $\Lambda$, $\Lambda$-ultrametric spaces have, among other reasons, appeared as a means of constructing structures with lattices of equivalence relations embedding $\Lambda$. This makes use of an isomorphism of…

A topological space is almost locally compact if it contains a dense locally compact subspace. We generalize a result from \cite{Ma}, showing that isomorphism on Borel classes of almost locally compact Polish metric structures is always…

In this paper, we investigate Kondratiev spaces on domains of polyhedral type. In particular, we will be concerned with necessary and sufficient conditions for continuous and compact embeddings, and in addition we shall deal with pointwise…

Given two compact n-dimensional manifolds in the smooth, piecewise linear or topological categories, basic results of B. Mazur and others give simple criteria for determining whether their products with Euclidean spaces of sufficiently…

We obtain an internal topological characterization of the subspaces of Eberlein compacts (respectively, Corson compacts, strong Eberlein compacts, uniform Eberlein compacts, $n$-uniform Eberlein compacts).

Complementing our previous results, we give a classification of all isometries (not necessarily surjective) of the metric space consisting of ball-bodies, endowed with the Hausdorff metric. "Ball bodies" are convex bodies which are…

We prove that if open subgroups of the groups of invertible elements in two Fourier-Stieltjes algebras are isometric as metric spaces, then the underlying locally compact groups are topologically isomorphic. We describe the structure of…

We first briefly review some aspects of the techniques of dealing with ultraviolet divergences in Feynman amplitudes in an Euclidian $D$-dimensional space-time. Next we consider compactification of a $d$-dimensional ($d\leq D$) subspace.…

We prove that compact Hausdorff spaces with a $\mathbb{P}$-diagonal are metrizable.

In a recent paper \cite{T} the fact that a class of locally compact metric spaces $X$, among which are Euclidean spaces, are not homemorphic to their punctured version $X\men\{p\}$, was given an interesting new proof which does not use…

We consider isometric immersions in arbitrary codimension of three-dimensional strongly pseudoconvex pseudo-hermitian CR manifolds into the Euclidean space $\mathbb{R}^n$ and generalize in a natural way the notion of associated family. We…

We show, by an elementary and explicit construction, that the group of Hamiltonian diffeomorphisms of certain symplectic manifolds, endowed with Hofer's metric, contains subgroups quasi-isometric to Euclidean spaces of arbitrary dimension.

This chapter reviews some past and recent developments in shape comparison and analysis of curves based on the computation of intrinsic Riemannian metrics on the space of curves modulo shape-preserving transformations. We summarize the…

We consider a complete biharmonic immersed submanifold $M$ in an Euclidean space $\mathbb{E}^N$. Assume that the immersion is proper, that is, the preimage of every compact set in $\mathbb{E}^N$ is also compact in $M$. Then, we prove that…

In this paper induced U-equivalence spaces are introduced and discussed. Also the notion of U-equivalently open subsets of a U-equivalence space and U-equivalently open functions are studied. Finally, equivalently uniformisable topological…

Extending the results of reconstruction of compact metric spaces by inverse limits, we show that if $(X, d), (Y, d)$ are compact metric spaces, then the mapping space $Y^X$ is homotopy equivalent to the inverse limit of an inverse system of…

We study the a.s. convergence of a sequence of random embeddings of a fixed manifold into Euclidean spaces of increasing dimensions. We show that the limit is deterministic. As a consequence, we show that many intrinsic functionals of the…

We introduce the notion of tiling spaces for metric spaces. The class of tiling spaces contains the Euclidean spaces, the middle-third Cantor set, and various self-similar spaces appearing in fractal geometry. For doubling tiling spaces, we…

We present a natural family of Hilbert function spaces on the d-dimensional complex unit ball and classify which of them satisfy that subsets of the ball yield isometrically isomorphic subspaces if and only if there is an analytic…