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  1. MHB Master
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    I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ...

    I am currently reading Chapter 3: Continuous Functions on Intervals and am currently focused on Section 3.1 Limits and Continuity ... ...

    I need some help in understanding the proof of Proposition 3.12 ...


    Proposition 3.12 and its proof read as follows:








    In the above proof by Browder we read the following:

    " ... ... Since $ \displaystyle f(I) \subset J$, $ \displaystyle f^{ -1 } ( g^{ -1 }(V) ) = f^{ -1 } (U) \cap f^{ -1 } (J) = f^{ -1 } (U)$ ... ... "


    My question is as follows:

    Can someone please explain exactly why/how $ \displaystyle f^{ -1 } (U) \cap f^{ -1 } (J) = f^{ -1 } (U)$ ... ...



    Help will be much appreciated ...

    Peter

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