For reference, here is problem 5 from the previous homework: This is a continuation of Problem 5

For reference, here is problem 5 from the previous homework:

Transcribed Image Text:

This is a continuation of Problem 5 from the previous homework. Let A C R be an open subset. Prove that a function f: A → R is continuous if and only if for every open subset UCR, the pre-image f(U) C A is open. This is a continuation of Problem 5 from the previous homework. Let A C R be an open subset. Prove that a function f: A → R is continuous if and only if for every open subset UCR, the pre-image f(U) C A is open.