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Math Help - Basic Topology, closed and open sets

  1. #1
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    Question Basic Topology, closed and open sets

    Consider the metric space ([0, 1], | |).In this space, no number smaller than 0 or more than 1 exists.

    a) Show that any interval in the form (r,s), where 0 < r < s < 1 is open in this space.

    b)Show that any interval in the form [0, s), where s < 1, is open in this space.

    c) Show that any interval in the form (r, 1], where r > 0, is open in this space.
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  2. #2
    Junior Member Dark Sun's Avatar
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    Hello, there may be a simpler way, but this proved it for me:

    a) Let y\in (r,s). Then, for \delta =\min \{d(r,y),d(s,y)\}, we have that B_d(y,\delta )\subset (r,s), hence (r,s) is open.

    For b) and c), adapt the same argument accordingly.
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