continuity of a function; uniform topology on R^\omega

Consider in the standard topology and in the uniform topology.

Consider the function given by .

QUESTION: Is continuous??

MY ATTEMPT:

Let where .

Let .

To see whether is open in or not.

I have worked out that , where

Using this i proved that

I am not able to see whether is open in or not. Can someone please help me on this??

Re: continuity of a function; uniform topology on R^\omega

Okay i think i've got it. 'g' is continuous.

Anyways.. thanks to anyone who cared to have a look.

Re: continuity of a function; uniform topology on R^\omega

why you did not try to prove that g is continuous at every point x in R

g is continuous at x ( x in the domain sure ) if for every open set "v" containing g(x) we can find an open set "u" in

R such x u and g(u) v

how is the open sets in the uniform topology ?