Timeline for The tangent bundle to an infinite-dimensional manifold
Current License: CC BY-SA 3.0
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| Dec 23, 2016 at 18:22 | comment | added | Pedro Lauridsen Ribeiro | If you use the Whitney topology on $C^\infty(A,B)$, the modelling topological vector spaces are the spaces $\Gamma^\infty_c(f^*TB)$ of smooth sections of $f^*TB$ with compact support, $f\in C^\infty(A,B)$. In order to get a smooth manifold structure, one needs to use the so-called $c^\infty$ topology on $\Gamma^\infty_c(f^*TB)$, which is the final topology induced by all smooth curves therein and therefore finer than its standard topology. Nonetheless, for this particular modelling vector space, kinematical and operational tangent vectors do coincide. | |
| Jun 27, 2011 at 11:02 | history | answered | Andrew Stacey | CC BY-SA 3.0 |