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inknit
#7
Mar2-12, 12:37 PM
P: 59
Quote Quote by Bacle2 View Post
"now, Is there any constant that is not continuous?"

Try this:

f:X-->Y , f(x)=c , constant.

Use the inverse open set definition: V open in Y; then you have two main options:

i)V contains c.

ii)V does not contain c.

What can you say about f-1(V)?
The preimage of V has to be either X or the empty set.