A Countable Interpolation Problem

A Basic Interpolation Problem

A basic interpolation problem, which includes bitangential matrix versions of a number of classical interpolation problems, is formulated and solved. Particular attention is placed on the development of the problem in a natural way and upon the fundamental role played by a special class of reproducing kernel Hilbert spaces of vector-valued meromorphic functions that originate in the work of L. ...

The Point - Countable Base Problem

On a Geometrical Interpolation Problem

Given a finite set of points A in R and a geometrical pattern Φ we define a type of distance between A and Φ and study how to find a pattern Φ among a parametrized family of geometrical objects such that such a distance is minimum. Mathematics Subject Classification: 41A29

Chapter 14 The Point - Countable Base Problem

The Homeomorphism Problem for Countable Topological Spaces

We consider the homeomorphism problem for countable topological spaces and investigate its descriptive complexity as an equivalence relation. It is shown that even for countable metric spaces the homeomorphism problem is strictly more complicated than the isomorphism problem for countable graphs and indeed it is not Borel reducible to any orbit equivalence relation induced by a Borel action of ...