Every locale (frame) is a dense sublocale of a spatial subfit one

Abstract

This paper answers a long standing open problem regarding which pointfree topologies (locales) can, or cannot, be embedded into subfit locales. Subfitness, a point-free weak separation property closely related to T ₁ , is well-known to be non-hereditary. So, the problem amounts to characterizing just how badly non-hereditary the property is.