Stone space, often denoted as \( \beta X \), is a concept from topology and set theory that arises in the context of the study of completely regular spaces and the construction of compactifications. The Stone space is a specific type of space associated with a totally bounded and complete metric space or, more generally, with a completely regular Hausdorff space.
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A Stone space is a compact Hausdorff space that is totally disconnected, equivalently a compact Hausdorff space with a basis of clopen sets. The topology on a type space gives an important example.