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Continuous mappings between spaces of arcs

2012/01/13 by Goulwen Fichou, Fichou, Goulwen, Masahiro Shiota +1
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #math.AG

paper · pdf · doi:10.48550/arxiv.1201.2775

openalex publication_date 2012/01/13 · arxiv created 2013/05/29 · arxiv updated 2013/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A blow-analytic homeomorphism is an arc-analytic subanalytic homeomorphism, and therefore it induces a bijective mapping between spaces of analytic arcs. We tackle the question of the continuity of this induced mapping between the spaces of arcs, giving a positive and a negative answer depending of the topology involved. We generalise the result to spaces of definable arcs in the context of o-minimal structures, obtaining notably a uniform continuity property.

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