Covering properties of Cp(X) and Ck(X)

Abstract

Let X be a Tychonoff space. We survey some classic and recent results that
characterize the topology or cardinality of X when Cp(X) or Ck(X) is covered by certain families of sets (sequences, resolutions, closure-preserving coverings, compact coverings ordered by a second countable space) which swallow or not some classes of sets (compact sets, functionally bounded sets, pointwise bounded sets) in C (X).