From 19329aafb4480de872c1565e12fb2b1172c22d09 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Thu, 12 Mar 2026 16:08:47 -0500 Subject: [PATCH 1/4] add "crowded" and "dense-in-itself" aliases --- properties/P000139.md | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/properties/P000139.md b/properties/P000139.md index decdcdd94b..c4c9802ecb 100644 --- a/properties/P000139.md +++ b/properties/P000139.md @@ -1,6 +1,12 @@ --- uid: P000139 name: Has an isolated point +aliases: +- Not crowded +- Not dense-in-itself +refs: +- mathse: 3823020 + name: Reference request: crowded space --- Some singleton $\{x\}\subseteq X$ is an open set. From 48f306963d86536e04c89aed1921c24c2fece148 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Thu, 12 Mar 2026 16:11:05 -0500 Subject: [PATCH 2/4] fix yaml --- properties/P000139.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/properties/P000139.md b/properties/P000139.md index c4c9802ecb..5b55fc09f2 100644 --- a/properties/P000139.md +++ b/properties/P000139.md @@ -6,7 +6,7 @@ aliases: - Not dense-in-itself refs: - mathse: 3823020 - name: Reference request: crowded space + name: "Reference request: crowded space" --- Some singleton $\{x\}\subseteq X$ is an open set. From 5af71b93605b3e8e6d4dca88e397860256fcf21f Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Thu, 12 Mar 2026 21:00:50 -0500 Subject: [PATCH 3/4] Implement @prabau's suggestions --- properties/P000139.md | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) diff --git a/properties/P000139.md b/properties/P000139.md index 5b55fc09f2..2ad0f71450 100644 --- a/properties/P000139.md +++ b/properties/P000139.md @@ -7,8 +7,14 @@ aliases: 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}. \ No newline at end of file +*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}. From 98f3df38d776c3f101bded5b5715de5313409dd1 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Thu, 12 Mar 2026 21:37:20 -0500 Subject: [PATCH 4/4] Update properties/P000139.md Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> --- properties/P000139.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/properties/P000139.md b/properties/P000139.md index 2ad0f71450..1fe0a4d06c 100644 --- a/properties/P000139.md +++ b/properties/P000139.md @@ -8,7 +8,7 @@ refs: - mathse: 3823020 name: "Reference request: crowded space" - wikipedia: Dense-in-itself - name: "Dense in itself on Wikipedia" + name: "Dense-in-itself on Wikipedia" --- Some singleton $\{x\}\subseteq X$ is an open set.