For a topological space , it is a natural undertaking to compare its topology with the weak topology generated by a family of real-valued continuous functions on . We present a necessary and sufficient condition for the coincidence of these topologies for an arbitrary family . As a corollary, we give a new proof of the fact that families of functions which separate points on a compact space induce topologies that coincide with the original topology.
"A necessary and sufficient condition for coincidence with the weak topology." Involve 10 (2) 257 - 261, 2017. https://doi.org/10.2140/involve.2017.10.257