diff --git a/properties/P000105.md b/properties/P000105.md
index 1a873b5a8..585f29173 100644
--- a/properties/P000105.md
+++ b/properties/P000105.md
@@ -6,7 +6,10 @@ refs:
   name: Encyclopedia of general topology (Hart et al)
 ---
 
-Every open cover of the space has a locally countable open refinement.
+Every open cover of $X$ has a locally countable open refinement.
+
+(A collection $\mathscr V$ of subsets of $X$ is *locally countable*
+if each $x\in X$ has a neighborhood meeting at most countably many elements of $\mathscr V$.)
 
 Defined on page 200 of {{zb:1059.54001}}.
 
diff --git a/theorems/T000587.md b/theorems/T000587.md
deleted file mode 100644
index 26025a9c8..000000000
--- a/theorems/T000587.md
+++ /dev/null
@@ -1,9 +0,0 @@
----
-uid: T000587
-if:
-  P000018: true
-then:
-  P000083: true
----
-
-Evident from the definitions, as a countable cover is point-countable.
diff --git a/theorems/T000654.md b/theorems/T000654.md
index dee89ef9b..3eab1c60a 100644
--- a/theorems/T000654.md
+++ b/theorems/T000654.md
@@ -6,4 +6,4 @@ then:
   P000105: true
 ---
 
-Immediate from definitions.
+Immediate from the definitions.
diff --git a/theorems/T000655.md b/theorems/T000655.md
index 26ce117b4..45c40679f 100644
--- a/theorems/T000655.md
+++ b/theorems/T000655.md
@@ -6,4 +6,4 @@ then:
   P000083: true
 ---
 
-Immediate from definitions.
+Immediate from the definitions.