LAUSR

Abstract A set Y ⊂ C p ( X ) is uniformly dense in C p ( X ) if it is dense in the uniform topology on C ( X ) . We construct a zero-dimensional σ-compact space X such that C p ( X ) has a uniformly dense Lindelof subspace while C p ( X ) is not normal. This example answers several published open questions. Additionally, we obtain a version of a theorem of Reznichenko on ω-monolithicity, under M A + ¬ C H , of a compact space X if C p ( X ) has a uniformly dense Lindelof subspace. We also prove that if X is a dyadic compact then C p ( X ) has a uniformly dense subspace of countable pseudocharacter.