Two equivalent metrics can be compared, with respect to their uniform properties, in several different ways. We present some of them, and then use one of these conditions to characterize which metrics on a space induce the same lower Hausdorff topology on the hyperspace. Finally, we focus our attention to complete metrics.

This paper proposes a self-stabilizing edge coloring algorithm using (Δ + 4) colors for distributed systems of a planar graph topology, where Δ ≥ 5 is the maximum degree of the graph. The algorithm can be applied to anonymous uniform systems and its time complexity is O(n 2) moves under the central daemon model.

A Tychonoff space $X$ is called $\kappa$-pseudocompact if for every continuous mapping $f$ of into $\mathbb{R}^\kappa$ the image $f(X)$ compact. This notion generalizes pseudocompactness and gives a stratification spaces lying between pseudocompact compact spaces. It well known that determined by uniform structure function $C_p(X)$ real-valued functions on endowed with pointwise topology. In re...

This paper describes a multiresolution method for implicit curves and surfaces The method is based on wavelets and is able to simplify the topology The implicit curves and surfaces are de ned as the zero valued algebraic isosurface of a tensor product uniform cubic Bspline A wavelet multiresolution method that deals with uniform cubic Bsplines on bounded domains has been constructed Further the...

This paper deals with uniform synchronization analysis of multi-agent systems with switching topologies. The agents are assumed to have general, yet identical, linear dynamics. The underlying communication topology may switch arbitrarily within a finite set of admissible topologies. We establish conditions under which the network is uniformly synchronized meaning that synchronization is valid u...

We review some of the most striking properties of the phase diagrams of higher dimensional black holes in pure gravity. We focus on static black hole solutions with KaluzaKlein asymptotics and stationary black hole solutions in flat Minkowski space. Both cases exhibit a rich pattern of interconnected phases and merger points with topology changing transitions. In the first case, the phase diagr...

Using Toruńczyk’s charaterization theorem, we show that the space CB(X,Y ) of bounded continuous mappings from X into Y is a topological manifold modelled on the Hilbert space of weight 20 , with respect to the topology of uniform convergence, under the following three assumptions: (1) X is a noncompact, separable and metrizable space, (2) Y is a complete metric space which is an ANRU (ANR in u...

The Bohl algebra B is the ring of linear combinations of functions te on the real line, where k is any nonnegative integer, and λ is any complex number, with pointwise operations. We show that the Bass stable rank and the topological stable rank of B (where we use the topology of uniform convergence) are infinite.

We derive various inequalities involving the intersection number of the curves contained in geodesics and tight geodesics in the curve graph. While there already exist such inequalities on tight geodesics, our method applies in the setting of geodesics. Furthermore, the method gives inequalities with a uniform constant depending only on the topology of the surface.

This paper presents a distributed mobile storage system designed for storage elements connected by a network of non-uniform quality. Flexible data placement is crucial, and it leads to challenges for locating data and keeping it consistent. Our system employs a locationand topology-sensitive multicast-like solution for locating data, lazy peer-to-peer propagation of invalidation information for...