[分析] 問一題點拓撲

[ikikiki (小優)]

(a) Let K be a compact set in R^3 and define

        C={(x,y) in R^2 | there exists z in R such that (x,y,z) in K}

    Prove that C is a compact set in R^2.



(b) Let A be a path connected subset of R^n and f:A→R^m be a continuous

    function. Define the graph of f by


       G={(u,v) in R^n+m | u in A , v=f(u)}

    Prove that G is path connected.


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