pi-base · prabau · Jan 28, 2026 · Jan 27, 2026 · Jan 27, 2026 · Jan 28, 2026
diff --git a/properties/P000028.md b/properties/P000028.md
@@ -4,6 +4,8 @@ name: First countable
 refs:
   - zb: "0386.54001"
     name: Counterexamples in Topology
+  - zb: "0684.54001"
+    name: General Topology (Engelking, 1989)
 ---
 
 A space with a countable local basis at every point.
@@ -17,3 +19,4 @@ Defined on page 7 of {{zb:0386.54001}}.
 - A space that is locally {P28} (every point has a neighborhood with the property)
 has the property.
 - $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
+- This property is preserved by countable products. (Corollary 2.3.14 in {{zb:0684.54001}})
diff --git a/spaces/S000054/properties/P000050.md b/spaces/S000054/properties/P000050.md
diff --git a/spaces/S000076/properties/P000028.md b/spaces/S000076/properties/P000028.md
@@ -2,12 +2,6 @@
 space: S000076
 property: P000028
 value: true
-refs:
-- zb: "0386.54001"
-  name: Counterexamples in Topology
 ---
 
-$X$ is a product of first countable spaces.
-
-Asserted in the General Reference Chart for space #84 in
-{{zb:0386.54001}}.
+$X$ is the square of {S43} and {S43|P28}.
diff --git a/spaces/S000076/properties/P000050.md b/spaces/S000076/properties/P000050.md
@@ -2,10 +2,6 @@
 space: S000076
 property: P000050
 value: true
-refs:
-- zb: "0386.54001"
-  name: Counterexamples in Topology
 ---
 
-Asserted in the General Reference Chart for space #84 in
-{{zb:0386.54001}}.
+$X$ is the square of {S43} and {S43|P50}.
diff --git a/spaces/S000076/properties/P000065.md b/spaces/S000076/properties/P000065.md
@@ -2,10 +2,6 @@
 space: S000076
 property: P000065
 value: true
-refs:
-- zb: "0386.54001"
-  name: Counterexamples in Topology
 ---
 
-Asserted in the General Reference Chart for space #84 in
-{{zb:0386.54001}}.
+Since $\mathfrak{c} \cdot \mathfrak{c} = \mathfrak{c}$.