Some Topologically Invariant Metric Properties

On a Metric on Translation Invariant Spaces

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

Topologically Left Invariant Mean on Dual Semigroup Algebras

Some Properties of Median Metric Spaces

We decribe a number of properties of a median metric space. In particular, we show that a complete connected median metric of finite rank admits a cononical bilipschitz equivalent CAT(0) metric. Metric spaces of this sort arise, up to bilipschitz equivalence, as asymptotic cones of certain classes of finitely generated groups, and the existence of such a structure has various consequences for t...

Some Metric Properties of Automorphisms of Groups

Study of the dynamics of automorphisms of a group is usually focused on their growth and/or finite orbits, including fixed points. In this paper, we introduce properties of a different kind; using somewhat informal language, we call them metric properties. Two principal characteristics of this kind are called here the “curl” and the “flux”; there seems to be very little correlation between thes...

Some topological properties of fuzzy strong b-metric spaces

‎In this study‎, ‎we investigate topological properties of fuzzy strong‎ b-metric spaces defined in [13]‎. ‎Firstly‎, ‎we prove Baire's theorem for‎ ‎these spaces‎. ‎Then we define the product of two fuzzy strong b-metric spaces‎ ‎defined with same continuous t-norms and show that $X_{1}times X_{2}$ is a‎ ‎complete fuzzy strong b-metric space if and only if $X_{1}$ and $X_{2}$ are‎ ‎complete fu...