Open Research Index

Perfect surjections and paracompactness

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

Palomar Registrypalomar/PALOMAR-2026-10-13-000004Oct 13, 2026math.GNscore 0

A continuous closed surjection from a Hausdorff space, with compact fibres, preserves and reflects ordinary open-cover paracompactness. The paracompact image is proved Hausdorff without assuming target separation. Supporting selected results give inverse transfer without separation or surjectivity, forward transfer to a regular target, local finiteness of images of arbitrary indexed families, and the regular-space criterion using arbitrary locally finite refinements. No metrizability, countability, local compactness or uniform fibre-size assumption is imposed. The source is based on Munkres…

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