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Math Help - Discrete Topology

  1. #1
    Junior Member
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    Unhappy Discrete Topology

    (b) If A, as a subspace of X, has discrete topology, then X has discrete topology.
    False. X= Q(Rational Numbers) and A = Z(Integers) (My Guess)

    (c) If X has discrete topology then every subspace of X has discrete topology.
    True.

    I don't know to get these answers can someone plz give me a hint
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by Dreamer78692 View Post
    (b) If A, as a subspace of X, has discrete topology, then X has discrete topology.
    False. X= Q(Rational Numbers) and A = Z(Integers) (My Guess)

    Right. (I suppose the usual topology on \mathbb{Q}) .


    (c) If X has discrete topology then every subspace of X has discrete topology.True.

    True, if B\subset A then, B=A\cap B and A is open in X .
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