1. ## Uniformly continuous functions

Hi! Help me please to solve this.
Prove or disprove that:

1. If $f,g$ are uniformly continuous functions in $[0,\infty )$ then also $fg$ (product) is unif.continuous in $[0,\infty )$.

2. Same question, but about the composition of $f$ and $g$.

Thanks beforehand.

2. ## Re: Uniformly continuous functions

Originally Posted by sinichko
Hi! Help me please to solve this.
Prove or disprove that:
1. If $f,g$ are uniformly continuous functions in $[0,\infty )$ then also $fg$ (product) is unif.continuous in $[0,\infty )$.
2. Same question, but about the composition of $f$ and $g$.
Can you do this question if you drop the word uniformly?
If so, try to use those proofs. If not, look up those proofs.
Then post what you have done here,