From 9f06f864312332e07cc32080a7987b2882dba85a Mon Sep 17 00:00:00 2001 From: yhx-12243 Date: Sat, 13 Sep 2025 08:21:40 +0800 Subject: [PATCH 1/4] =?UTF-8?q?Strengthen=20T664=20(Monotonically=20normal?= =?UTF-8?q?=20=E2=87=92=20Shrinking)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- theorems/T000664.md | 12 ++++-------- 1 file changed, 4 insertions(+), 8 deletions(-) diff --git a/theorems/T000664.md b/theorems/T000664.md index debbd2655c..f80b83ebea 100644 --- a/theorems/T000664.md +++ b/theorems/T000664.md @@ -3,14 +3,10 @@ uid: T000664 if: P000109: true then: - P000032: true + P000193: true refs: - - doi: 10.1016/C2009-0-12309-7 - name: Handbook of Set-Theoretic Topology (Kunen & Vaughan) - - mathse: 5012078 - name: High-level overview and detailed proof that monotonically normal spaces are countably paracompact + - zb: "0769.54022" + name: Monotone normality (Balogh & Rudin) --- -See Theorems 1.2 and 2.3 of Chapter 17 of {{doi:10.1016/C2009-0-12309-7}}. - -See also {{mathse:5012078}} for a more detailed explanation. +See Corollary 2.2 of {{zb:0769.54022}}. From d9a24872fd3b34dc1bb3821941e6c35c4c7138e1 Mon Sep 17 00:00:00 2001 From: yhx-12243 Date: Fri, 19 Dec 2025 19:37:16 +0800 Subject: [PATCH 2/4] feat: comments --- theorems/T000664.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/theorems/T000664.md b/theorems/T000664.md index c328b9baa3..11fc49f603 100644 --- a/theorems/T000664.md +++ b/theorems/T000664.md @@ -15,4 +15,6 @@ See Theorems 1.2 and 2.3 of Chapter 17 of {{doi:10.1016/C2009-0-12309-7}}. See also {{mathse:5012078}} for a more detailed explanation. -Compare with {T805} and {T543}, which is a refinement of this result. +Compare with {T805} and {T543}, which constitute a refinement of this result. + + From 14bce17aecfd19358281c27098abebe71220c415 Mon Sep 17 00:00:00 2001 From: Moniker1998 <88507423+Moniker1998@users.noreply.github.com> Date: Tue, 30 Dec 2025 08:29:42 +0100 Subject: [PATCH 3/4] another characterization of GO-space --- properties/P000154.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/properties/P000154.md b/properties/P000154.md index 361709ad38..0197bb1662 100644 --- a/properties/P000154.md +++ b/properties/P000154.md @@ -24,6 +24,8 @@ and every point has a local base of order-convex neighborhoods. Equivalently, $X$ is homeomorphic to a subspace of a {P133}. +Equivalently, $X$ is homeomorphic to a closed subspace of a {P133}. + For more details and the proof of these equivalences, see {{zb:0228.54026}} () and {{mathse:4917398}}. From 5f031058de916ecc602f70a6b084ca4b7043e426 Mon Sep 17 00:00:00 2001 From: Moniker1998 <88507423+Moniker1998@users.noreply.github.com> Date: Tue, 30 Dec 2025 17:31:27 +0100 Subject: [PATCH 4/4] Added Kemoto as reference --- theorems/T000805.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/theorems/T000805.md b/theorems/T000805.md index 0d819eb2e0..bc49c76171 100644 --- a/theorems/T000805.md +++ b/theorems/T000805.md @@ -7,6 +7,8 @@ then: refs: - zb: "0769.54022" name: Monotone normality (Balogh & Rudin) + - zb: "0761.54022" + name: The shrinking property and the B-property in ordered spaces (Kemoto) --- -See Corollary 2.2 of {{zb:0769.54022}}. +See corollary 2.2 of {{zb:0769.54022}}. The proof for {P154} is corollary 2.2 in {{zb:0761.54022}}.