On countably saturated and pre-dyadic spaces

In this paper, we introduce a new class of spaces which extends the class of dyadic compacta. This permits to extend a classical theorem of Engelking and Pe & lstrok;czy & nacute;ski. Technically, our arguments are based on the concept of a countably saturated space. This is a space in which the closure of every countable subset is a metrizable compactum. The existence of a dense countably saturated subspace in compact Hausdorff spaces is shown below to play a crucial role. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.