let c be a field of subsets of a set i. also, let     1 i i be a non-decreasing positivesequence of real numbers such that 1, 1 0 1   i  and    11 i i . in this paper we prove thatbv of all the games of -bounded variation on c is a non-separable and norm dual banach space of thespace of simple games on c . we use this fact to establish the existence of a linear mapping t from...

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...

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...

We propose to measure band topology via quantized drift of Bloch oscillations in a two-dimensional Harper-Hofstadter lattice subjected tilted fields both directions. When the difference between two is large, uniformly sample all momenta, and hence displacement each direction tends be at multiples overall period, regardless any momentum initial state. The related reduced Chern number defined as ...

A celebrated theorem of Marshall Hall Jr. implies that finitely generated free groups are subgroup separable and that all of their finitely generated subgroups are retracts of finite-index subgroups. We use topological techniques inspired by the work of Stallings to prove that all limit groups share these two properties. This answers a question of Sela. Limit groups are finitely presented group...

modeling and simulation of processing plants are widely used in industry. construction of a mathematical model for a plant is a time-consuming and error-prone task. in light of extensive advancements in computer science (both hardware and software), computers are becoming a necessary instrument in industrial activities. many software tools for modeling, simulation and optimization of processing...

Certain subclasses of B 1 (K), the Baire-1 functions on a compact metric space K, are defined and characterized. Some applications to Banach spaces are given. Let X be a separable infinite dimensional Banach space and let K denote its dual ball, Ba(X *), with the weak* topology. K is compact metric and X may be naturally identified with a closed subspace of C(K). X * * may also be identified wi...

We prove that the locally convex space $C_{p}(X)$ of continuous real-valued functions on a Tychonoff $X$ equipped with topology pointwise convergence is distinguished if and only $\Delta$-space in sense \cite {Knight}. As an application this characterization theorem we obtain following results: 1) If \v{C}ech-complete (in particular, compact) such $C_p(X)$ distinguished, then scattered. 2) For ...

The establishment and growth of an early Australian entrepreneurial firm supplying veterinary services and products is examined. John Pottie established a veterinary practice in Sydney in the 1860's and then proceeded to develop a large and successful family business that is still trading. By exploring the ingredients for its successful entry and growth, this study seeks to show through one lon...