Okay i think i've got it. 'g' is continuous.
Anyways.. thanks to anyone who cared to have a look.
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??
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 ?