# zbMATH — the first resource for mathematics

Hereditary $$\kappa$$-separability and the hereditary $$\kappa$$-Lindelöf property in function spaces. (English) Zbl 0666.54003
This paper is concerned with the smallest linear subspace $$L_ p(X)$$ of $$C_ pC_ p(X)$$ containing the Tychonoff space X. It is proved that $$L_ p(X)$$ is hereditarily $$\kappa$$-Lindelöf (hereditarily $$\kappa$$- separable, resp.) if and only if $$X^{\omega}$$ is hereditarily $$\kappa$$- Lindelöf (hereditarily $$\kappa$$-separable, resp.). Moreover, it is shown that a certain cardinal function of $$L_ p(X)$$ called the weak pseudonet weight of $$L_ p(X)$$ equals the net weight of X.
##### MSC:
 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) 54C35 Function spaces in general topology
Full Text: