Recent content by im2fastfouru

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    Understanding Inverse Images and Continuity in Real Analysis

    1. a) Show that (f^-1 S)compliment = f^-1(S compliment) for any set S of reals. Then use part a) to show The function f is continuous iff f^-1(S) is closed for every closed set S. 2. inverse image = f^-1(S) = {x: f(x) \in S} f is continuous iff for every open set U \in the reals...
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    Graduate Is f continuous if f^-1(S) is closed for all closed sets S?

    Any help on this problem would be appreciated a) Show that (f^-1 S)compliment is equal to f^-1(S compliment) for any set S of reals. Then use part a) to show The function f is continuous iff f^-1(S) is closed for every closed set S.
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    Undergrad Product of two continous functions

    There is a proof in my book that asks us to prove that the product of two continuous functions is continuous. If anyone could help please reply back, thanks!
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    Undergrad Proving Power Set Inclusion: A Simple Proof for A⊆B and P(A)⊆P(B)

    x is just an arbitrary element. And if A \subseteq B then prove P(A) \subseteq P(B). This need to be proved formally as well for my assignment!
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    Undergrad Proving Power Set Inclusion: A Simple Proof for A⊆B and P(A)⊆P(B)

    i'm more inclined to start with x \in P(a), can i start the proof this way?
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    Undergrad Proving Power Set Inclusion: A Simple Proof for A⊆B and P(A)⊆P(B)

    This seems like a simple proof but I'm not familiar with power set proofs If A\subseteqB then P(A) \subseteq P(B)