diff --git a/properties/P000154.md b/properties/P000154.md index 361709ad3..0197bb166 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}}. diff --git a/theorems/T000664.md b/theorems/T000664.md index debbd2655..11fc49f60 100644 --- a/theorems/T000664.md +++ b/theorems/T000664.md @@ -14,3 +14,7 @@ refs: 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 constitute a refinement of this result. + + diff --git a/theorems/T000805.md b/theorems/T000805.md new file mode 100644 index 000000000..bc49c7617 --- /dev/null +++ b/theorems/T000805.md @@ -0,0 +1,14 @@ +--- +uid: T000805 +if: + P000109: true +then: + P000193: true +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}}. The proof for {P154} is corollary 2.2 in {{zb:0761.54022}}.