fix P39, P40

pi-base · Oct 9, 2024 · e75d92e · e75d92e
1 parent 0816725
commit e75d92e
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diff --git a/spaces/S000199/properties/P000039.md b/spaces/S000199/properties/P000039.md
@@ -4,5 +4,6 @@ property: P000039
 value: true
 ---
 
-Every pair of basic open sets $(\leftarrow,m)$ and $(\leftarrow,n)$
-intersects.
+The topology is a chain under inclusion;
+that is,
+for each pair of open sets, one is contained in the other.
diff --git a/spaces/S000199/properties/P000040.md b/spaces/S000199/properties/P000040.md
@@ -4,4 +4,6 @@ property: P000040
 value: true
 ---
 
-$0$ is in the closure of every non-empty set.
+The collection of closed sets is a chain under inclusion;
+that is,
+for each pair of closed sets, one is contained in the other.
diff --git a/spaces/S000200/properties/P000039.md b/spaces/S000200/properties/P000039.md
@@ -4,5 +4,6 @@ property: P000039
 value: true
 ---
 
-Every pair of basic open sets $[m,\rightarrow)$ and $[n,\rightarrow)$
-intersects.
+The topology is a chain under inclusion;
+that is,
+for each pair of open sets, one is contained in the other.
diff --git a/spaces/S000200/properties/P000040.md b/spaces/S000200/properties/P000040.md
@@ -4,6 +4,6 @@ property: P000040
 value: true
 ---
 
-Let $m\in M$ and $n\in N$ be members of closed sets $M,N$.
-Then every neighborhood of $m$ contains $n$, so $m$ is a
-limit point of $N$, showing $m\in M\cap N$.
+The collection of closed sets is a chain under inclusion;
+that is,
+for each pair of closed sets, one is contained in the other.