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metric spaces proof watch

    • Thread Starter

    hello there,
    Does anyone know how to prove the following. We haven't really covered enough of the necessary material yet and I'm really struggling to prove it.

    " Let X, Y and Z be metric spaces and let f: X -> Y and g: Y -> Z be continuous maps. Using the open set characterisation of continuity, prove that the composition mapping gof : X -> Z is continuous."

    If you know how to prove this, I would really appreciate any help.
    Thank you very much for your time.

    Well, what do you know that might be useful? [I'm thinking, what do you know about continuous functions that links preimages of open sets, to other open sets].
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Updated: March 1, 2006

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