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?
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 ???
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?
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?