The main object of the paper is to study the distance between Banach spaces introduced by Kadets. For Banach spaces X and Y , the Kadets distance is defined to be the infimum of the Hausdorffâ€¦ (More)

It is proved that there exist complemented subspaces of countable topo-logical products (locally convex direct sums) of Banach spaces which cannot be represented as topological products (locallyâ€¦ (More)

The main purpose of the paper is to develop an approach to the evaluation or the estimation of the spanning tree congestion of planar graphs. This approach is used to evaluate the spanning treeâ€¦ (More)

The main purpose of the paper is to prove the following results: â€¢ Let A be a locally finite metric space whose finite subsets admit uniformly bilipschitz embeddings into a Banach space X. Then Aâ€¦ (More)

The main purpose of the paper is to construct a sequence of graphs of constant degree with indefinitely growing girths admitting embeddings into `1 with uniformly bounded distortions. This resultâ€¦ (More)

max(u,v)âˆˆE |f(u)âˆ’ f(v)| if p = âˆž. If G is connected, then the only functions f satisfying ||f ||E,p = 0 are constant functions, so || Â· ||E,p is a norm on each linear space of functions on VG whichâ€¦ (More)

The main purpose of the paper is to find some expansion properties of locally finite metric spaces which do not embed coarsely into a Hilbert space. The obtained result is used to show that infiniteâ€¦ (More)

For a Banach space X we shall denote the set of all closed subspaces of X by G(X). In some kinds of problems it turned out to be useful to endow G(X) with a topology. The main purpose of the presentâ€¦ (More)