Continuous mappings between spaces of arcs

Goulwen Fichou (1) , Masahiro Shiota (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Graduate School of Mathematics [Nagoya]

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.

Mots clés: blow-analytic homeomorphism; arc space; real closed field; o-minimal structure

Domaines: Géométrie algébrique [math.AG]

Goulwen Fichou, Masahiro Shiota. Continuous mappings between spaces of arcs. 2012. ⟨hal-00659415v3⟩