Abstract
If a Tychonoff space X has a point-countable network of cardinality ≤ℵ1 and Y is a normal dense subspace of Cp(X), then Y is collectionwise normal. If a Tychonoff space X has a point-countable network of cardinality ≤ℵ1, then Cp(Cp(X)) also has a point-countable network of cardinality ≤ℵ1. We prove these statements and obtain some corollaries on equivalence of normality and collectionwise normality for dense subspaces of Cp,n(X).
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