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Dowker's countable paracompactness, product normality and strict insertion characterization

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

Palomar Registrypalomar/PALOMAR-2026-10-12-000003Oct 12, 2026math.GNscore 0

Formalization of Dowker (1951), Theorem 4: normality plus ordinary countable paracompactness of an arbitrary topological space X is equivalent to normality of X times the closed unit interval, and to strict continuous insertion between arbitrary real upper and lower semicontinuous functions h<g. No T1 or Hausdorff assumption on X, boundedness or uniform gap is added. Companion compact metrizable product theorem (Lemma 3) and countable-cover/decreasing-closed-sequence equivalences (Theorem 2) are included.

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