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arXiv · 1201.2775

Continuous mappings between spaces of arcs

Goulwen Fichou·Masahiro Shiota
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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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Goulwen Fichou, Masahiro Shiota. 2013-05-29. Continuous mappings between spaces of arcs. https://arxiv.org/abs/1201.2775

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