diff --git a/theorems/T000650.md b/theorems/T000650.md index 62a46fc8d..5b71d50b7 100644 --- a/theorems/T000650.md +++ b/theorems/T000650.md @@ -1,9 +1,9 @@ ---- -uid: T000650 -if: - P000208: true -then: - P000016: true ---- - -By definition. +--- +uid: T000650 +if: + P000208: true +then: + P000016: true +--- + +By definition. diff --git a/theorems/T000652.md b/theorems/T000652.md index e89f0151e..bd7ddc1de 100644 --- a/theorems/T000652.md +++ b/theorems/T000652.md @@ -1,10 +1,10 @@ ---- -uid: T000652 -if: - P000208: true -then: - P000130: true ---- - -For each $x \in X$, the set of open neighborhoods of $x$ is a local basis of compact neighborhoods, since every open set is compact. - +--- +uid: T000652 +if: + P000208: true +then: + P000130: true +--- + +For each $x \in X$, the set of open neighborhoods of $x$ is a local basis of compact neighborhoods, since every open set is compact. + diff --git a/theorems/T000657.md b/theorems/T000657.md index d33b381fd..47dcdeed5 100644 --- a/theorems/T000657.md +++ b/theorems/T000657.md @@ -1,9 +1,9 @@ ---- -uid: T000657 -if: - P000208: true -then: - P000131: true ---- - -By definition, because a compact space is Lindelöf. +--- +uid: T000657 +if: + P000208: true +then: + P000131: true +--- + +By definition, because a compact space is Lindelöf.