Finite unions of locally nice spaces

Embeddings of Locally Finite Metric Spaces into Banach Spaces

We show that if X is a Banach space without cotype, then every locally finite metric space embeds metrically into X.

Topology on locally finite metric spaces

The necessity of a theory of General Topology and, most of all, of Algebraic Topology on locally finite metric spaces comes from many areas of research in both Applied and Pure Mathematics: Molecular Biology, Mathematical Chemistry, Computer Science, Topological Graph Theory and Metric Geometry. In this paper we propose the basic notions of such a theory and some applications: we replace the cl...

Finite unions of submodules ON FINITE UNIONS OF SUBMODULES

This paper is concerned with finite unions of ideals and modules. The first main result is that if N ⊆ N1 ∪N2 ∪ · · · ∪Ns is a covering of a module N by submodules Ni, such that all but two of the Ni are intersections of strongly irreducible modules, then N ⊆ Nk for some k. The special case when N is a multiplication module is considered. The second main result generalizes earlier results on co...

Metrisability of Unions of Spaces

Finite Unions of Interpolation Sequences

A unified and relatively simple proof is given for some well-known results involving finite unions of uniformly separated sequences. In this note we consider finite unions of uniformly separated sequences, which appear in several well-known theorems involving both Hardy and Bergman spaces. The techniques of proof, some of which are quite involved, differ greatly from result to result. The purpo...