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.
© 2014 Asuman G. Aksoy, Jose M. Almira
A. G. Aksoy, J. Almira, On approximation schemes and compactness, Proceedings of the first conference on classical and functional analysis, Azuga-Romania, pp. 5-24, 2014,