Continuous mappings between spaces of arcs
Algebraic Geometry
2013-05-30 v4
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.
Cite
@article{arxiv.1201.2775,
title = {Continuous mappings between spaces of arcs},
author = {Goulwen Fichou and Masahiro Shiota},
journal= {arXiv preprint arXiv:1201.2775},
year = {2013}
}