In Micheal C. Gemignani, "Elementary Topology" in section 1.1 there is the following exercise(adsbygoogle = window.adsbygoogle || []).push({});

2)

i)

If [tex]f:S \rightarrow T[/tex] and [tex]G: T \rightarrow W [/tex], then [tex](g \circ f)^{-1}(A) = f^{-1}(g^{-1}(A))[/tex] for any [tex]A \subset W [/tex].

I think the above is only true if A is in the image of g yet the book says to prove the above. I have what I believe is a counter example. Any comments? I will give people two days to prove the above or post a counter example. After this time I'll post my counter example for further comment.

**Physics Forums - The Fusion of Science and Community**

# Composition of Inverse Functions

Know someone interested in this topic? Share a link to this question via email,
Google+,
Twitter, or
Facebook

Have something to add?

- Similar discussions for: Composition of Inverse Functions

Loading...

**Physics Forums - The Fusion of Science and Community**