no. 2
Continuous mappings between spaces of arcs
[Applications continues entre espaces d'arcs]
Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 2, pp. 315-337

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.

Un homéomorphisme analytique après éclatements est en particulier analytique par arcs et sous-analytique, il induit donc une application bijective entre les espaces d'arcs analytiques associés. On étudie la continuité de cette application induite, en fonction de la topologie considérée. On considère également la généralisation au cadre o-minimal, obtenant ainsi une propriété de continuité uniforme.

Publié le :
DOI : 10.24033/bsmf.2689
Classification : 14P15
Keywords: Blow-analytic homeomorphism, arc space, real closed field, o-minimal structure
Mots-clés : Homéomorphisme analytique après éclatements, espace d'arcs, corps réel clos, structure o-minimale 
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     title = {Continuous mappings between spaces of arcs},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {315--337},
     year = {2015},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {143},
     number = {2},
     doi = {10.24033/bsmf.2689},
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Fichou, Goulwen; Shiota, Masahiro. Continuous mappings between spaces of arcs. Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 2, pp. 315-337. doi: 10.24033/bsmf.2689

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