Timeline for Manifolds of continuous mappings.
Current License: CC BY-SA 2.5
3 events
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| Sep 2, 2010 at 18:58 | comment | added | Andrew Stacey | The great thing about the calculus of Kriegl, Michor, Frolicher (and others) is that continuity is secondary. So worrying about whether or not a map is continuous or what topology to put on L(X,Y) is no longer relevant. What matters is the effect on smooth curves, and in that realm then the exponential law holds and the derivative can be viewed in both ways. | |
| Sep 2, 2010 at 15:25 | comment | added | Pietro Majer | Thank you, I'll have a good reading! I think I once had a glance to 3. Isn't that an important feature of these works is the differential of $f:U\subset X\to Y$ as a map $Df:U\times X\to Y$ rather than a map $Df:U\to L(X,Y)$? (which in infinite dimension really makes a different notion of a continuously differentiable map)? | |
| Sep 2, 2010 at 11:02 | history | answered | Andrew Stacey | CC BY-SA 2.5 |