show long circle is T5 but not perfectly normal

properties/P000015.md

@@ -8,6 +8,8 @@ refs:
     name: General Topology (Engelking, 1989)
   - mathse: 72138
     name: Why are these two definitions of a perfectly normal space equivalent?
+  - mathse: 1840621
+    name: Answer to "Perfectly Normal is hereditary"
 ---
 
 A space $X$ for which, for any disjoint closed sets $A$ and $B$, there is a
@@ -20,3 +22,9 @@ in Theorem 1.5.19 of {{zb:0684.54001}} (under the assumption of a {P2} space, bu
 equally valid without this assumption).  See also {{mathse:72138}}.
 
 Defined on page 16 of {{doi:10.1007/978-1-4612-6290-9}} (as perfectly \(T_4\)).
+
+----
+
+#### Meta-properties
+
+- This property is hereditary (see {{mathse:1840621}}).

properties/P000067.md

@@ -12,6 +12,13 @@ refs:
     name: Normal space on Wikipedia
 ---
 
-A space that is both {P2} and {P15}. Equivalently, a space that is both {P1} and {P15}.
+A space that is both {P2} and {P15}.
+Equivalently, a space that is both {P1} and {P15}.
 
 Defined on page 16 of {{doi:10.1007/978-1-4612-6290-9}} as "perfectly normal".
+
+----
+
+#### Meta-properties
+
+- This property is hereditary since {P2} and {P15} are.

properties/P000081.md

@@ -7,3 +7,9 @@ refs:
 ---
 
 For each $A\subseteq X$ and each $p\in \overline A$ there is a countable subset $D\subseteq A$ such that $p\in \overline D$.
+
+----
+
+#### Meta-properties
+
+- This property is hereditary.

spaces/S000196/properties/P000008.md

@@ -0,0 +1,7 @@
+---
+space: S000196
+property: P000008
+value: true
+---
+
+Every proper subspace is {P154} and thus {P7}.

spaces/S000196/properties/P000081.md

@@ -0,0 +1,8 @@
+---
+space: S000196
+property: P000081
+value: false
+---
+
+This space contains a copy of {S36}, and
+{S36|P81}.