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add "crowded" and "dense-in-itself" aliases #1673

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Merged
prabau merged 4 commits into from
Mar 13, 2026
Merged

add "crowded" and "dense-in-itself" aliases #1673

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19329aa
add "crowded" and "dense-in-itself" aliases
StevenClontz Mar 12, 2026
48f3069
fix yaml
StevenClontz Mar 12, 2026
5af71b9
Implement @prabau's suggestions
StevenClontz Mar 13, 2026
98f3df3
Update properties/P000139.md
StevenClontz Mar 13, 2026
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14 changes: 13 additions & 1 deletion properties/P000139.md
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@@ -1,8 +1,20 @@
---
uid: P000139
name: Has an isolated point
aliases:
- Not crowded
- Not dense-in-itself
refs:
- mathse: 3823020
name: "Reference request: crowded space"
- wikipedia: Dense-in-itself
name: "Dense-in-itself on Wikipedia"
---

Some singleton $\{x\}\subseteq X$ is an open set.

Compare with {P107}.
*Note*: A space that fails to satisfy {P139},
i.e., a space without any isolated points, is called "dense-in-itself" or "crowded".
See {{wikipedia:Dense-in-itself}} and {{mathse:3823020}}.

Compare with {P107}.
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