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Perfect images of metrizable spaces

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

Palomar Registrypalomar/PALOMAR-2026-10-15-000016Oct 15, 2026math.GNscore 0

Every continuous closed surjection with compact fibers from an arbitrary metrizable space has a metrizable codomain. A new uniform shrinking-star estimate for compact-fiber metric neighborhoods constructs a sigma locally finite open basis on the image. A proper-map formulation and an actual compatible metric are included. No second countability, separability, compact domain, local compactness, completeness, finite-fiber or nonemptiness assumption is made. Target separation is derived. Classical mathematics; no novelty or priority claim.

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