Monday, 21 April 2014

functional analysis - Prove sets of continuous mappings are the same


Let C([0,T];C(¯U)) denote the set of all continuous functions u:[0,T]C(¯U) with
uC([0,T];C(¯U)):=max0tTu(t)<



Prove that C([0,T];C(¯U))=C([0,T]ׯU)





I am skeptical this is even true. I feel like we could apply a theorem from topology regarding the product space, but am having little success. Not really sure how to approach such a problem. Are there any counter examples that disprove the above? Any help would be much appreciated.

No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find limh0sin(ha)h without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...