Keywords
Cp(X)
Ck(X)
P-space
almost P-space
F-space.
Ck(X)
P-space
almost P-space
F-space.
Abstract
For a topological space X, let P be an ideal of closed sub-sets of X and Cp(X) be the ideal of C(X) of all functions f such that the support o f Flies in P. In this paper, we investigate the ideals of C(X) which are of the form Cp (X ) for some ideal P of closed sub-sets of X. We characterize P-spaces and almost P-spaces in terms of the ideals of the fom Cp( X) . Examples and counter examples are given.