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fix P193 def
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ccaruvana authored Sep 28, 2024
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name: Shrinking space
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A space in which every open cover admits a shrinking; that is, a space $X$ in which, given any open cover $\mathscr U$, there is a function $s : \mathscr U \to \tau_X \setminus \{\emptyset\}$ such that $s[\mathscr U]$ is an open cover and, for each $U \in \mathscr U$, $\mathrm{cl}_X s(U) \subseteq U$.
A space in which every open cover admits a shrinking; that is, a space $X$ in which, given any open cover $\mathscr U$, there is a function $s : \mathscr U \to \tau_X$ such that $s[\mathscr U]$ is an open cover and, for each $U \in \mathscr U$, $\mathrm{cl}_X s(U) \subseteq U$.

See also [Dan Ma's Topology Blog post on Spaces with shrinking properties](https://dantopology.wordpress.com/2017/01/05/spaces-with-shrinking-properties/).

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