This is an announcement for the paper "On approximation schemes and compactness" by A. G. Aksoy and J. M. Almira.

Abstract: We present an overview of some results about characterization of compactness in which the concept of approximation scheme has had a role. In particular, we present several results that were proved by the second author, jointly with Luther, a decade ago, when these authors were working on a very general theory of approximation spaces. We then introduce and show the basic properties of a new concept of compactness, which was studied by the first author in the eighties, by using a generalized concept of approximation scheme and its associated Kolmogorov numbers, which generalizes the classical concept of compactness.

Archive classification: math.FA

Remarks: 18 pages, submitted

Submitted from: jmalmira@ujaen.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1311.2385

or

http://arXiv.org/abs/1311.2385