Topological basis problem under determinacy

Abstract We study the topological basis problem under ZF, the Zermelo‐Fraenkel axiomatic set theory without the Axiom of Choice. We prove that under AD+, the class of regular topologies on has a three element basis and the class of Hausdorff topologies on has a single‐element basis. In particular, AD+ implies that the class of uncountable regular spaces has a four element basis.