few claims need to check if it is right

• Oct 24th 2008, 01:00 PM
szpengchao
few claims need to check if it is right
A continuous function on closed bounded X subset of R is uniformly convergent.

i mean,

a uniformly convergent sequence of functions must converge to a uniformly continuous function.
• Oct 24th 2008, 01:08 PM
Plato
Quote:

Originally Posted by szpengchao
The uniform limit of uniformly continuous function is continuous.

A continuous function on closed bounded X subset of R is uniformly convergent.

• Oct 24th 2008, 01:21 PM
Plato
Quote:

Originally Posted by szpengchao
A continuous function on closed bounded X subset of R is uniformly convergent.
a uniformly convergent sequence of functions must converge to a uniformly continuous function.

If that is your meaning of "uniform limit", then the limit function is continuous.

A continuous function on closed bounded X subset of R is uniformly continuous.
This is also true because closed bounded X subset of R are compact.
• Oct 24th 2008, 04:47 PM
szpengchao
ok.
Quote:

Originally Posted by Plato
If that is your meaning of "uniform limit", then the limit function is continuous.

A continuous function on closed bounded X subset of R is uniformly convergent.
This is also true because closed bounded X subset of R are compact.

Are you sure that the second one is true?

i mean, uniformly convergent. not uniformly continuous.
• Oct 25th 2008, 04:34 AM
Plato
I have corrected that typo.