The main purpose of this study is to introduce the absolute Lucas series spaces and investigate their some algebraic topological structure such as inclusion relations, $BK-$ space, duals Schauder basis. Also, characterizations matrix operators related these space with norms are given. Finally, by using Hausdorff measure noncompactness, necessary sufficient conditions for a operator on them be c...

In this paper, we give a characterization of compact sets in Lp-spaces on metric measure spaces, which is generalization the Kolmogorov-Riesz theorem. Using criterion, investigate topological type space consisting Lipschitz maps with bounded supports.

The present paper is mainly concerned with establishing conditions which .assure that all lattice regular measures have additional smoothness properties or that simply all two-valued such measures have such properties and are therefore Dirac measures. These conditions are expressed in terms of the general Wallman space. The general results are then applied to specific topological lattices, yiel...

We consider a randomly forced Ginzburg–Landau equation on an unbounded domain. The forcing is smooth and homogeneous in space and white noise in time. We prove existence and smoothness of solutions, existence of an invariant measure for the corresponding Markov process and we define the spatial densities of topological entropy, of measure-theoretic entropy, and of upper box-counting dimension. ...

For any countable group, and also for any locally compact second countable, compactly generated topological group, G, we show the existence of a “universal” hypercyclic (i.e. topologically transitive) representation on a Hilbert space, in the sense that it simultaneously models every possible ergodic probability measure preserving free action of G.

Each homeomorphism from the n-dimensional Sierpiński gasket into itself is a similarity map with respect to the usual metrization. Moreover, the topology of this space determines a kind of Haar measure and a canonical metric. We study spaces with similar properties. It turns out that in many cases, “fractal structure” is not a metric but a topological phenomenon.

This article is divided into two parts. In the first part, we prove some useful theorems on finite topological spaces. In the second part, in order to consider a family of neighborhoods to a point in a space, we extend the notion of finite topological space and define a new topological space, which we call formal topological space. We show the relation between formal topological space struct (F...

We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in descriptive set theoretic (topological) sense and in measure theoretic sense. In particular, it gives a new perspective on Vershik’s theorems on genericity and randomness of Urysohn’s space among separable metric spaces.

It is argued that quantum gravity has an interpretation as a topological quantum field theory provided a certain constraint from the path integral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for space time dimensions different from 3. We then discuss possible models which may be relevant to our universe. E-mail: [email protected]

We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in discriptive set theoretic (topological) sense and in measure theoretic sense. In particular, it gives a new perspective on Vershik’s theorems on genericity and randomness of Urysohn’s space among separable metric spaces.