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Generalized Whitney topologies are Baire


Authors: Edson de Faria and Peter Hazard
Journal: Proc. Amer. Math. Soc. 148 (2020), 5441-5455
MSC (2010): Primary 58C07; Secondary 54E52, 46E35, 26A16
DOI: https://doi.org/10.1090/proc/15168
Published electronically: August 14, 2020
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Abstract: In this paper we show that certain generalizations of the $ C^r$-Whitney topology, which include the Hölder-Whitney and Sobolev-Whitney topologies on smooth manifolds, satisfy the Baire property, to wit, the countable intersection of open and dense sets is dense.


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Additional Information

Edson de Faria
Affiliation: Instituto de Matemática e Estatística, USP, São Paulo, SP, Brazil
MR Author ID: 357550
Email: edson@ime.usp.br

Peter Hazard
Affiliation: Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, RJ, Brazil
MR Author ID: 950009
Email: peterh@id.uff.br

DOI: https://doi.org/10.1090/proc/15168
Keywords: Genericity, Whitney topology, H\"older classes, Sobolev classes.
Received by editor(s): October 4, 2018
Received by editor(s) in revised form: April 26, 2020
Published electronically: August 14, 2020
Additional Notes: This work has been supported by “Projeto Temático Dinâmica e Geometria em Baixas Dimensões” FAPESP Grant 2016/25053-8, FAPESP Grant 2015/17909-7, CAPES Grant CSF-PVE-S - 88887.117899/2016-00, a CAPES/PNPD Grant and the EU Marie-Curie IRSES Brazilian-European partnership in Dynamical Systems (FP7-PEOPLE-2012-IRSES 318999 BREUDS)
Communicated by: Nimish Shah
Article copyright: © Copyright 2020 American Mathematical Society