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Update properties/P000225.md
Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com>
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Equivalently, $X$ is locally contractible at each of its points. A space $X$ is *locally contractible at a point* $x \in X$ if every neighborhood $U$ of $x$ contains a neighborhood $V$ of $x$ such that the inclusion map $V \to U$ is null-homotopic.
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This is the standard definition of "locally contractible" in the theory of ANRs. Defined as "locally contractible" on page 28 of {{zb:0153.52905}}, page 347 of {{zb:"1280.54001"}}, and page 341 of {{zb:"1059.54001"}}.
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This is the standard definition of "locally contractible" in the theory of ANRs, as originally introduced by Borsuk. Defined as *locally contractible* on page 28 of {{zb:0153.52905}}, page 347 of {{zb:1280.54001}}, and page 341 of {{zb:1059.54001}}.
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#### Meta-properties

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