Open Research Index

Brouwer characterization of Cantor space

Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

Palomar Registrypalomar/PALOMAR-2026-10-23-000001Oct 23, 2026math.GNscore 0

A topological space is homeomorphic to Cantor space, the countable product of discrete Boolean spaces, if and only if it is nonempty, compact, metrizable, has a basis of clopen sets, and has no isolated points. A full binary clopen scheme decides an enumerated basis one element at each depth. Its point-address map is continuous; compact nested intersections realize every binary branch, and basis decisions separate points. A continuous bijection from a compact space to the Hausdorff Cantor space is a homeomorphism. This formalizes a classical theorem of Brouwer; no mathematical novelty or…

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