Kuratowski reduction in a σ-frame

Kuratowski introduced the reduction property for a class of pointsets in 1936, and established a sufficient condition for a class to possess this property. The reduction property became a cornerstone of classical descriptive set theory. We show that Kuratowskiʼs original argument is really a result in σ-frames. This provides a characterization of strongly zero-dimensional completely regular frames. Even for spaces, this connection with Kuratowski reduction has apparently not been acknowledged in the literature.