Discrete Generators

A subset G of C(X), the set of all continuous real-valued functions on a space X is a generator provided: whenever a point x is not in a closed set C then for some g in G we have g(x) not in the closure of g(C). Equivalently G is a generator if {g^(-1) U : U open in R and g in G} is a base for X.

With the topology of pointwise convergence C(X) becomes a space, Cp(X), and every generator picks up the subspace topology.  In this talk we investigate which spaces have a discrete generator. (Joint work with Ziqin Feng and Alex Yuschik.)