Timeline for On the definition of convergence of a sequence of sections of a bundle
Current License: CC BY-SA 3.0
4 events
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| Jun 25, 2014 at 14:33 | comment | added | Ali Taghavi | @RafeMazzeo I think that you do not mean the following:"If a compact topological space admit two compatible metrics $d_{1}, d_{2}$, then two metrics are equivalent, that is $\frac{d_{1}}{d_{2}}$ is bounded from below and above" There is a counter example for this statement. | |
| Nov 19, 2013 at 5:03 | comment | added | Rafe Mazzeo | Once one chooses trivializations of bundles, coordinates, etc., then this reduces to the standard real analysis exercise that if $f_1$ and $f_2$ are two strictly positive functions on a compact set $K$, then there exist positive constants $C_1$, $C_2$ such that $C_1 f_1 \leq f_2 \leq C_2 f_1$. Similarly, if $A_1$ and $A_2$ are two positive definite matrices depending smoothly on a compact set $K$, then $C_1 A_1 \leq A_2 \leq C_2 A_1$ (where $A \leq B$ means $\langle Av,v \rangle \leq \langle Bv, v\rangle$). | |
| Nov 19, 2013 at 4:46 | comment | added | Sepideh Bakhoda | Where can I find proof of your claim? It is extremely important for me. thanks in advance. | |
| Nov 7, 2013 at 21:31 | history | answered | Rafe Mazzeo | CC BY-SA 3.0 |