If f and g are two uniformly continuous functions, I need to show that their product is also uniformly continuous. I started with the definition of uniform continuity but got nowhere...

Printable View

- Mar 20th 2010, 08:25 PMCrazyCat87Multiplying Uniformly Continuous functions
If f and g are two uniformly continuous functions, I need to show that their product is also uniformly continuous. I started with the definition of uniform continuity but got nowhere...

- Mar 20th 2010, 08:58 PMTinyboss
You're not going to get anywhere, either, unless you restrict the domain. Is uniformly continuous on ? What about ?

- Mar 21st 2010, 04:28 PMCrazyCat87
Sorry I'm not sure what you mean by that...

- Mar 21st 2010, 04:30 PMTinyboss
Let be given by . Is f uniformly continuous? What about the product of f with f?

- Mar 23rd 2010, 05:45 PMCrazyCat87
yea I haven't figured it out yet... it's probably simple but i'm having a lot of trouble with this one

- Mar 23rd 2010, 07:04 PMKrizalid
is trivially uniformly continuous since so the product is not uniformly continuous, namely is not uniformly continuous.

- Mar 23rd 2010, 08:00 PMCrazyCat87
lol but this is isn't making sense since I'm supposed to show the product IS uniformly continuous

- Mar 24th 2010, 07:32 AMKrizalid
IT'S NOT TRUE, and i've provided a counterexample.

- Mar 24th 2010, 02:09 PMCrazyCat87
lol you're right, now what if both functions were bounded?

- Mar 25th 2010, 07:43 PMphuongtim39
I accept with information: http://www.mathhelpforum.com/math-he...300389f6-1.gif is trivially uniformly continuous since http://www.mathhelpforum.com/math-he...48476b03-1.gif

_________________

Argentina adventure tours