diff --git a/properties/P000090.md b/properties/P000090.md index e0c9be11da..8feb1fffac 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. + +This is equivalent to each of the following: -* 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..f74ab566f8 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. + +This is equivalent to each of the following: -- 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..d70846551d 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}. + +This is equivalent to each of the following: -- 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..448a83d04f 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. + +This is equivalent to each of the following: -- 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.