# Can someone give an example on uniformly bounded sequence but not equicontinuous at 0

• April 20th 2010, 08:33 AM
copyfriend
Can someone give an example on uniformly bounded sequence but not equicontinuous at 0
Can someone give an example on uniformly bounded sequence of continuous functions on B(0,1) but not equicontinuous at 0?

Thanks everyone.
• April 20th 2010, 12:40 PM
Opalg
Quote:

Originally Posted by copyfriend
Can someone give an example on uniformly bounded sequence of continuous functions on B(0,1) but not equicontinuous at 0?

How about $f_n(x) = \sin nx$?