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    Sets and containment

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    C = containment
    int = interior
    ext = exterior
    cl = closure

    Could you please prove if S C T, then
    a)int(S) C int(T)
    b)ext(T) C ext(S)
    c)cl(S) C cl(T)

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    Solution Preview

    S C T means S is a subset of T.
    (a) for any x in int(S), x is an interior point of S, this means we can find an open set U which contains x and U belongs to S. But S belongs to T. So U also belongs to T. Thus x is an ...

    Solution Summary

    This is a set regarding containment and closure.