I think there is some sort of subtlety I'm missing, because it seems like the following example would be non-continuous under the current definition:
X = [0,1]
Y = Real numbers
f(x) = 0 (constant for all x in [0,1]).
Then if U = (-1,1), U is open and in Y, but yet F^-1(U) = {0} which is not open.
A constant function is not continuous!? What is wrong? |
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