From 11737821df5822a8d56f81868e7d3cb293b8f085 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Fri, 13 Dec 2024 19:51:09 -0600 Subject: [PATCH 1/2] better first lines for properties with multiple characterizations --- properties/P000090.md | 5 +++-- properties/P000185.md | 5 +++-- properties/P000195.md | 5 +++-- properties/P000196.md | 5 +++-- 4 files changed, 12 insertions(+), 8 deletions(-) diff --git a/properties/P000090.md b/properties/P000090.md index e0c9be11da..481f21fc70 100644 --- a/properties/P000090.md +++ b/properties/P000090.md @@ -11,9 +11,10 @@ aliases: - Alexandroff-discrete --- -Any of the following equivalent properties holds: +An arbitrary intersection of open sets is open. + +Or, any of the following equivalent properties holds: -* An arbitrary intersection of open sets is open. * An arbitrary union of closed sets is closed. * Each $x \in X$ has a unique smallest neighborhood. * For each $A \subseteq X$, $A$ is open iff $A \cap Y$ is open in the subspace $Y$ for each finite $Y \subseteq X$. diff --git a/properties/P000185.md b/properties/P000185.md index 325c99d54e..e8321e96a2 100644 --- a/properties/P000185.md +++ b/properties/P000185.md @@ -8,9 +8,10 @@ refs: name: On ultrapseudocompact and related spaces (T. Nieminen) --- -Any of the following equivalent properties holds: +There exists a basis for the topology that is also a partition into disjoint sets. + +Or, any of the following equivalent properties holds: -- There exists a basis for the topology that is also a partition into disjoint sets. - Every open set is closed. - Every closed set is open. - The space's Kolmogorov quotient is {P52}. diff --git a/properties/P000195.md b/properties/P000195.md index b8e3a31204..bbc01494ba 100644 --- a/properties/P000195.md +++ b/properties/P000195.md @@ -13,9 +13,10 @@ refs: name: Stone space on Wikipedia --- -Any of the following equivalent properties holds: +The space is {P16}, {P3}, and {P47}. + +Or, any of the following equivalent properties holds: -- The space is {P16}, {P3}, and {P47}. - The space is {P16} and {P48}. - The space is {P16}, {P1}, and {P50}. - The space is {P75} and {P2}. diff --git a/properties/P000196.md b/properties/P000196.md index 957361c341..67c7255463 100644 --- a/properties/P000196.md +++ b/properties/P000196.md @@ -8,9 +8,10 @@ refs: name: On ultrapseudocompact and related spaces (T. Nieminen) --- -Any of the following equivalent properties holds: +Every subspace is connected. + +Or, any of the following equivalent properties holds: -- Any subspace is connected. - The open sets are totally ordered by inclusion. - The closed sets are totally ordered by inclusion. - The specialization preorder is total. From fbe7194aa79aee9730a591b0e148e6ba68d40cb7 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Sat, 14 Dec 2024 11:10:38 -0600 Subject: [PATCH 2/2] reword equivalency lines --- properties/P000090.md | 2 +- properties/P000185.md | 2 +- properties/P000195.md | 2 +- properties/P000196.md | 2 +- 4 files changed, 4 insertions(+), 4 deletions(-) diff --git a/properties/P000090.md b/properties/P000090.md index 481f21fc70..8feb1fffac 100644 --- a/properties/P000090.md +++ b/properties/P000090.md @@ -13,7 +13,7 @@ aliases: An arbitrary intersection of open sets is open. -Or, any of the following equivalent properties holds: +This is equivalent to each of the following: * An arbitrary union of closed sets is closed. * Each $x \in X$ has a unique smallest neighborhood. diff --git a/properties/P000185.md b/properties/P000185.md index e8321e96a2..f74ab566f8 100644 --- a/properties/P000185.md +++ b/properties/P000185.md @@ -10,7 +10,7 @@ refs: There exists a basis for the topology that is also a partition into disjoint sets. -Or, any of the following equivalent properties holds: +This is equivalent to each of the following: - Every open set is closed. - Every closed set is open. diff --git a/properties/P000195.md b/properties/P000195.md index bbc01494ba..d70846551d 100644 --- a/properties/P000195.md +++ b/properties/P000195.md @@ -15,7 +15,7 @@ refs: The space is {P16}, {P3}, and {P47}. -Or, any of the following equivalent properties holds: +This is equivalent to each of the following: - The space is {P16} and {P48}. - The space is {P16}, {P1}, and {P50}. diff --git a/properties/P000196.md b/properties/P000196.md index 67c7255463..448a83d04f 100644 --- a/properties/P000196.md +++ b/properties/P000196.md @@ -10,7 +10,7 @@ refs: Every subspace is connected. -Or, any of the following equivalent properties holds: +This is equivalent to each of the following: - The open sets are totally ordered by inclusion. - The closed sets are totally ordered by inclusion.