Functional countability and exponential separability of product spaces and subspaces
General Topology
2026-03-03 v1
Abstract
We investigate the behavior of functional countability and exponential separability in products and subspaces of topological spaces. We solve a problem of Tkachuk by showing that the product of functionally countable pseudocompact spaces is itself functionally countable. Solving another problem of Tkachuk, we show that it is independent of ZFC whether regular spaces which have all their subspaces functionally countable are hereditarily Lindel\"of. Finally, we prove that the -product of non-zero ordinals is exponentially separable, thereby extending a result of Kemoto and Szeptycki.
Cite
@article{arxiv.2603.02018,
title = {Functional countability and exponential separability of product spaces and subspaces},
author = {Rodrigo Hernández-Gutiérrez and Santi Spadaro},
journal= {arXiv preprint arXiv:2603.02018},
year = {2026}
}