# Math Help - Discrete Topology

1. ## 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

2. Originally Posted by Dreamer78692
(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 $X$ .