# Property S with subsets

## Theorem

Let $(X,d)$ be a metric space and let $Y \subset X$ have property S. Then for any $Z$ such that $Y \subset Z \subset \overline{Y}$, $Z$ has property $S$ and also $Z$ is a Peano space.

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Let $(X,d)$ be a metric space and let $Y \subset X$ have property S. Then for any $Z$ such that $Y \subset Z \subset \overline{Y}$, $Z$ has property $S$ and also $Z$ is a Peano space.

- This page was last edited on 23 September 2016, at 17:29.