ID 1431
FullText File
Title Alternative
EQUIVARIANT DEFINABLE C^r APPROXIMATION THEOREM, DEFINABLE C^rG TRIVIALITY OF G INVARIANT DEFINABLE C^r FUNCTIONS AND COMPACTIFICATIONS
Authors
DOI
Journal Title
Bulletin of the Faculty of Education, Wakayama University. Natural science
ISSN
13424645
NCID
AN00257977
Volume
55
Start Page
23
End Page
36
Published Date
2005-02-28
Language
eng
Abstract Alternative
Let G be a compact subgroup of GLn(R) and 0 &le; s < r < ∞. We prove that every definable C^SG map between affine definable C^rG manifolds is approximated in the definable C^s topology by definable C^rG maps. We show that each G invariant proper submersive surjective definable C^r function defined on an affine definable C^rG manifold is definably C^rG trivial. Moreover we prove that every noncompact affine definable C^rG manifold admits a unique affine definable CrG compactification up to definable CTG diffeomorphism when r &ge; 2.
Content Type
Departmental Bulletin Paper
Text Version
publisher
Accession No.
KJ00004292660