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



Prove that C([0,T];C(\overline{U}))=C([0,T]\times \overline{U})





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 lim_{hrightarrow 0}frac{sin(ha)}{h}

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