{"id":"palomar/PALOMAR-2026-10-15-000016","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/0d447f17a30963a050f80ceff6283db782921448/topology/perfect-metrizable-images","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-15-000016-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.GN","msc:54E35","msc:54C10","general-topology","perfect-maps","metrizable-spaces"],"score":0,"title":"Perfect images of metrizable spaces","trust":"high","domain":"math.GN","source":"palomar","authors":["Arthur Freitas Ramos","David Barros Hulak","Ruy Jose Guerra Barretto de Queiroz"],"reviews":0,"subject":"math.GN","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-15","reactions":{},"formalized":true,"formalizes":[{"title":"Geometric Aspects of General Topology, second-edition author manuscript (November 2, 2023)","identifier":"https://www.researchgate.net/publication/299698540_Metrization_and_Paracompact_Spaces","relationship":"formalizes"}]}