Posted by Zack Judson on October 16, 2007, 4:38 pm T 3 and 1/2 means completely regular AND T1 We did not prove that the restriction of a continuous map is continuous. (HW4 Ex 5c shows that if f is continuous and we restrict it to a closed set then the restriction is continuous.) If f is continuous at a point then the preimage of an open set need not be open. If x is in U and f(U) is not contained in V, it is still possible for f(x) to be in V.
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There were several common mistakes on Homework 5 that came up while grading problem 4:
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