# Thread: few claims need to check if it is right

1. ## 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.

2. 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.
Please define "uniform limit".

3. 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.

4. ## ok.

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.

5. I have corrected that typo.