Characterizing algebras of C ∞ -functions on manifolds

Peter W. Michor; Jiří Vanžura

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 3, page 519-521
  • ISSN: 0010-2628

Abstract

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Among all C ∞ -algebras we characterize those which are algebras of C ∞ -functions on second countable Hausdorff C ∞ -manifolds.

How to cite

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Michor, Peter W., and Vanžura, Jiří. "Characterizing algebras of $C^\infty $-functions on manifolds." Commentationes Mathematicae Universitatis Carolinae 37.3 (1996): 519-521. <http://eudml.org/doc/247941>.

@article{Michor1996,
abstract = {Among all $C^\infty $-algebras we characterize those which are algebras of $C^\infty $-functions on second countable Hausdorff $C^\infty $-manifolds.},
author = {Michor, Peter W., Vanžura, Jiří},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$C^\infty $-algebra; smooth manifold; -algebra; smooth manifold},
language = {eng},
number = {3},
pages = {519-521},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Characterizing algebras of $C^\infty $-functions on manifolds},
url = {http://eudml.org/doc/247941},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Michor, Peter W.
AU - Vanžura, Jiří
TI - Characterizing algebras of $C^\infty $-functions on manifolds
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 3
SP - 519
EP - 521
AB - Among all $C^\infty $-algebras we characterize those which are algebras of $C^\infty $-functions on second countable Hausdorff $C^\infty $-manifolds.
LA - eng
KW - $C^\infty $-algebra; smooth manifold; -algebra; smooth manifold
UR - http://eudml.org/doc/247941
ER -

References

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  1. Anderson F.W, Blair R.L., Characterizations of the algebra of all real valued continuous functions on a completely regular space, Illinois J. Math. 3 (1959), 121-133. (1959) Zbl0083.17403MR0100786
  2. Gillman L., Jerison M., Rings of Continuous Functions, Princeton (1960). (1960) Zbl0093.30001MR0116199
  3. Kainz G, Kriegl A., Michor P.W., C ∞ -algebras from the functional analytic viewpoint, J. Pure Appl. Algebra 46 (1987), 89-107. (1987) Zbl0621.46046MR0894394
  4. Lawvere F.W., Categorical Dynamics, Lectures given 1967 at the University of Chicago, reprinted in Topos Theoretical Methods in Geometry A. Kock Aarhus Math. Inst. Var. Publ. Series 30 Aarhus Universitet (1979). (1979) Zbl0403.18005MR0552656
  5. Moerdijk I., Reyes G.E., Models for Smooth Infinitesimal Analysis, Springer-Verlag (1991). (1991) Zbl0715.18001MR1083355
  6. Prasad P.K., Algebras of differentiable functions and algebras of Lipschitz functions, Indian. J. Pure Appl. Math. 16.4 (1985), 376-382. (1985) Zbl0573.46013MR0788817
  7. Pursell L.E., Algebraic structures associated with smooth manifolds, Thesis Purdue University (1952). (1952) 
  8. Shanks M.E., Rings of functions on locally compact spaces, Report no. 365, Bull. Amer. Math. Soc. 57 (1951), 295. (1951) 

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