| Title:
|
Characterizing algebras of $C^\infty$-functions on manifolds (English) |
| Author:
|
Michor, Peter W. |
| Author:
|
Vanžura, Jiří |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
519-521 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Among all $C^\infty$-algebras we characterize those which are algebras of $C^\infty$-functions on second countable Hausdorff $C^\infty$-manifolds. (English) |
| Keyword:
|
$C^\infty$-algebra |
| Keyword:
|
smooth manifold |
| MSC:
|
46J15 |
| MSC:
|
46J20 |
| MSC:
|
46M15 |
| MSC:
|
51K10 |
| MSC:
|
58A03 |
| MSC:
|
58A05 |
| MSC:
|
58B10 |
| idZBL:
|
Zbl 0881.58001 |
| idMR:
|
MR1426917 |
| . |
| Date available:
|
2009-01-08T18:25:52Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118859 |
| . |
| Reference:
|
[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. Zbl 0083.17403, MR 0100786 |
| Reference:
|
[2] Gillman L., Jerison M.: Rings of Continuous Functions.Princeton (1960). Zbl 0093.30001, MR 0116199 |
| Reference:
|
[3] Kainz G, Kriegl A., Michor P.W.: $C^\infty$-algebras from the functional analytic viewpoint.J. Pure Appl. Algebra 46 (1987), 89-107. Zbl 0621.46046, MR 0894394 |
| Reference:
|
[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). Zbl 0403.18005, MR 0552656 |
| Reference:
|
[5] Moerdijk I., Reyes G.E.: Models for Smooth Infinitesimal Analysis.Springer-Verlag (1991). Zbl 0715.18001, MR 1083355 |
| Reference:
|
[6] Prasad P.K.: Algebras of differentiable functions and algebras of Lipschitz functions.Indian. J. Pure Appl. Math. 16.4 (1985), 376-382. Zbl 0573.46013, MR 0788817 |
| Reference:
|
[7] Pursell L.E.: Algebraic structures associated with smooth manifolds.Thesis Purdue University (1952). |
| Reference:
|
[8] Shanks M.E.: Rings of functions on locally compact spaces.Report no. 365, Bull. Amer. Math. Soc. 57 (1951), 295. |
| . |
