# Rationals with subspace topology from the reals

Suppose $\mathbb{Q}$ is endowed with the subspace topology of$\mathbb{R}$ Does it follow that $\mathbb{Q}$ is connected?

MY attempt: We can sue fact that $\mathbb{Q}$ is countable and so $\mathbb{Q} = \bigcup \{x\}$. And singletons are connected. Can we conclude that the union is connected?

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No.$\ \ \ \ \$ –  bof Oct 29 '13 at 1:04

In the relative topology, $\mathbb{Q}$ is totally disconnected.

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some might say totally disconnected. –  Daniel Rust Oct 29 '13 at 1:07
Yerright. I meant "totally" in the sense that each point is a connected component. –  ncmathsadist Oct 29 '13 at 1:13