# Notes - Metric Spaces MT23, Subspaces

> Source: https://ollybritton.com/notes/uni/part-a/mt23/metric-spaces/notes/subspaces/ · Updated: 2023-07-20 · Tags: uni, notes

- [Course - Metric Spaces MT23](https://ollybritton.com/notes/uni/part-a/mt23/metric-spaces/)

### Flashcards
What does it mean for one metric space $(Y, d_Y)$ to be a subspace of another metric space $(X, d_X)$?::
$Y \subseteq X$ and $d_Y$ is the restriction of $d_X$ to $Y$.

Can you give an example of a set open in a subspace, but closed in the entire space?::
Let $Y \subseteq X$ where $Y = \mathbb R \times \{0\}$ and $X = \mathbb R^2$. Then $B_Y(0, 1)$ is an open subset of $Y$, but a closed subset of $X$.

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