EDB β€” 107

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Exercises

  1. [107] Prerequisites:[0PS].Let X be a vector space, let πœ™,πœ“ be two norms on it. Show that the topologies generated by πœ™ and πœ“ coincide, if and only if there exist 0<a<b such that

    (1)βˆ€x,  aπœ“(x)β‰€πœ™(x)≀bπœ“(x)  .
    3

    (When the relation ?? holds, we will say that the norms are ”equivalent”).

    Solution 1

    [108]

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