Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an e...

We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...

A systematic study is made of spectral measures in locally convex spaces which are countably additive for the topology of uniform convergence on bounded sets, briefly, the bounded convergence topology. Even though this topology is not compatible for the duality with respect to the pointwise convergence topology it turns out, somewhat surprisingly, that the corresponding L'-spaces for the spectr...

WSNs (Wireless Sensor Networks) have the characteristics of limited communication radius and easy invalidation. Aimed at these characteristics, based on complex networks theory, a topology evolution TEBAS (Topology Evolution of Wireless Sensor Networks Based on adaptive scale-free networks), which introduces fitness and local world and more suitable for WSNs than ERW (Topology Evolution by Rand...

We show that the quasiconvex subgroups in doubles of certain negatively curved groups are closed in the profinite topology. This allows us to construct the first known large family of hyperbolic 3-manifolds such that any finitely generated subgroup of the fundamental group of any member of the family is closed in the profinite topology.

In this article, topology optimization of two-dimensional (2D) building frames subjected to seismic loading is performed using the polygonal finite element method. Artificial ground motion accelerograms compatible with the design response spectrum of ASCE 7-16 are generated for the response history dynamic analysis needed in the optimization. The mean compliance of structure is minimized as a t...

Simulations are an important tool in network research. As the selected topology often influences the outcome of the simulation, realistic topologies are needed to produce realistic simulation results. Using several similarity metrics to compare artificially generated topologies with real world topologies this letter gives hints how to use the wide-spread topology generators BRITE, TIERS and GT-...

We provide a natural topology for a cone metric space and a noncompactness measure is defined for this space, which enables us to extend existing results for mappings and set-valued mappings defined on classical metric spaces. Moreover it is proved that the topology of any uniform topological space is generated by a cone metric. c ©2016 All rights reserved.