Approximation of real continuous functions on Lindelöf spaces

The conclusion of 1.4 asserts that A is sequentially dense in Cp(X) (= C(X) with the topology of pointwise convergence). When A is a lattice, the conclusion can be combined with Dini's Theorem to obtain density in Cc(X) (= C(X) with the compact-open topology). This allows the following estimate of the sequential density character of, e.g., Cc(X), for infinite Lindel6f X: it does not exceed the weight of X; it follows that the cardinal of C(X) does not exceed (weight X)1o, and with a result of Kruse, equality holds.