Density properties and points of uncountable order for families of open sets in function spaces

We characterize the given extent in finite powers of X in terms of the topology of Cp(X). It is shown that many properties of Cp(X) are determined by dense subsets of Cp(X). We introduce the density tightness and establish that for compact spaces of π-weight ⩽ω1 countable density tightness implies countable π-character.