For $G$ a topological group, existence theorems by Milnor (1956), Gelfand-Fuks (1968), and Segal (1975) of classifying spaces for principal $G$-bundles are generalized to $G$-spaces with torsion. Namely, any $G$-space approximately covered tubes (a generalization local trivialization) is the pullback universal space indexed orbit types cardinality cover. Lie via metric model we generalize corre...

We construct a natural diffusion on wide class of metric spaces generalising graphs, and show that its cover time admits an upper bound depending only the Hausdorff measure space.

In recent years, Scalable Vocabulary Tree (SVT) has been shown to be effective in image retrieval. However, for general images where the foreground is the object to be recognized while the background is cluttered, the performance of the current SVT framework is restricted. In this paper, a new image retrieval framework that incorporates a robust distance metric and information fusion is propose...

We discuss scaling limits of large bipartite planar maps. If p ≥ 2 is a fixed integer, we consider, for every integer n ≥ 2, a random planar map Mn which is uniformly distributed over the set of all rooted 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space consisting of the set of vertices of Mn, equipped with the graph distance rescaled by the factor n−1...

Received (received date) Revised (revised date) Communicated by (Name) The article analyzes similarity of closed polygonal curves in Frechet metric, which is stronger than the well-known Hausdorff metric and therefore is more appropriate in some applications. An algorithm that determines whether the Frechet distance between two closed polygonal curves with m and n vertices is less than a given ...

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a metric space. Further properties of this metric space are studied in the next papers. The importance of the work can be situated in fields such as cosmology, quan...

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a metric space. Further properties of this metric space are studied in the next papers. The importance of the work can be situated in fields such as cosmology, quan...

We introduce topological definitions of expansivity, shadowing, and chain recurrence for homeomorphisms. They generalize the usual definitions for metric spaces. We prove various theorems about topologically Anosov homeomorphisms (maps that are expansive and have the shadowing property) on noncompact and non-metrizable spaces that generalize theorems for such homeomorphisms on compact metric sp...

We define here e-chaos and study its interrelationships with P -chaos and Ruelle-Takens chaos. We show that a continuous self map f on a compact metric space is e-chaotic (P -chaotic) need not imply the induced map f̄ : K(X) → K(X) is e-chaotic (P -chaotic) and vice-versa, where K(X) is the space of all non-empty compact subsets of X endowed with Hausdorff metric. Mathematics Subject Classificat...

Explicit product formulas are obtained for families of multivariate polynomials which are orthogonal on simplices and on a parabolic biangle in R. These product formulas are shown to give rise to measure algebras which are hypergroups. The article also includes an elementary proof that the Michael topology for the space of compact subsets of a topological space (which is used in the definition ...