We define for a topological group G and a family of subgroups F two versions for the classifying space for the family F , the G-CW -version EF (G) and the numerable G-space version JF (G). They agree if G is discrete, or if G is a Lie group and each element in F compact, or if F is the family of compact subgroups. We discuss special geometric models for these spaces for the family of compact op...

We show that any quantum family of maps from a non commutative space to a compact quantum metric space has a canonical quantum semi metric structure.

A graph G on a topological space X as its set of vertices is clopen if the edge relation of G is a clopen subset of X2 without the diagonal. We study clopen graphs on Polish spaces in terms of their finite induced subgraphs and obtain information about their cochromatic numbers. In this context we investigate modular profinite graphs, a class of graphs obtained from finite graphs by taking inve...

today each city due to natural limitations, facilities and planning policies has different growth pattern which according to its spread, has different consequences and results. although there is a wide range of urban growth patterns, but the important thing is not diversity and number of models but is the absence of rules and methods of transition from one to another pattern (form). so this art...

A mapping T from a topological space X to a topological space Y is said to be compact if T (X) is contained in a compact subset of Y. The aim of the paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends ...

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

Let  $varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and  $H$ be a compact subgroup of $G$. For  an admissible wavelet $zeta$ for $varpi$  and $psi in L^p(G/H), 1leq p <infty$, we determine a class of bounded  compact operators  which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.

We construct a two discrete parameter family of compact minimal surfaces embedded in the Berger sphere which may be considered as analogue helicoidal Karcher-Scherk surfaces.

It is shown that for every k and every p ≥ q ≥ d + 1 there is a c = c(k, p, q, d) < ∞ such that the following holds. For every family H whose members are unions of at most k compact, convex sets in R in which any set of p members of the family contains a subset of cardinality q with a nonempty intersection there is a set of at most c points in R that intersects each member of H. It is also show...