This is the Question:

Let

Show that is NOT compact set in

My idea is to show that converge pointwise to , and

Where

Is this enough to show is NOT compact set in ???

And how do I state formally that converge pointwise to ???

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- May 5th 2012, 12:49 AMsweetadamShow {x_n} is NOT a compact set in C([0,1])
This is the Question:

Let

Show that is NOT compact set in

My idea is to show that converge pointwise to , and

Where

Is this enough to show is NOT compact set in ???

And how do I state formally that converge pointwise to ??? - May 5th 2012, 02:02 AMgirdavRe: Show {x_n} is NOT a compact set in C([0,1])
In fact converges pointwise to the constant function equal to . If the set was compact, we would be able to extract a uniformly convergent sub-sequence . This one should converge uniformly to . Do you see why it is not possible?

- May 5th 2012, 07:22 AMsweetadamRe: Show {x_n} is NOT a compact set in C([0,1])
Thank you for fast reply :)

I'm really new to these concepts, sorry if my answer is silly lol

from the of uniform convergence:

for any and any

therefore no sub-sequence converge to 0 uniformly, hance is not compact

Is this right? - May 5th 2012, 08:21 AMgirdavRe: Show {x_n} is NOT a compact set in C([0,1])
That right.