diff --git a/properties/P000062.md b/properties/P000062.md
index 50c50008d8..687421c5bb 100644
--- a/properties/P000062.md
+++ b/properties/P000062.md
@@ -13,3 +13,4 @@ Every open cover of $X$ has a countable subcollection whose union is dense in $X
 
 - This property is hereditary with respect to clopen sets.
 - This property is preserved in any coarser topology.
+- If a nonempty product space satisfies the property, so does every factor.
diff --git a/properties/P000166.md b/properties/P000166.md
index 430c93239b..6179bbc085 100644
--- a/properties/P000166.md
+++ b/properties/P000166.md
@@ -17,4 +17,4 @@ the function space $C_p(X)$ being {P26}.
 #### Meta-properties
 
 - This property is preserved by countable disjoint unions.
-- This property is hereditary (use the fact that [Metrizable + Separable => Hereditarily separable](https://topology.pi-base.org/spaces?q=metrizable+%2B+Separable+%2B+%7EHereditarily+separable)).
+- This property is hereditary (use the fact that [Metrizable + Separable ⇒ Hereditarily separable](https://topology.pi-base.org/spaces?q=metrizable+%2B+Separable+%2B+%7EHereditarily+separable)).
diff --git a/properties/P000206.md b/properties/P000206.md
index b3afcfa705..c79651315d 100644
--- a/properties/P000206.md
+++ b/properties/P000206.md
@@ -26,3 +26,4 @@ to the {{wikipedia:Normal_play_convention}} of combinatorial games.
 #### Meta-properties
 
 - $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
+- This property is preserved by arbitrary products and box products.
diff --git a/spaces/S000077/README.md b/spaces/S000077/README.md
index 2356481c8f..f09d913c9f 100644
--- a/spaces/S000077/README.md
+++ b/spaces/S000077/README.md
@@ -1,9 +1,11 @@
 ---
 uid: S000077
-name: Michael's product topology
+name: Product of Michael line and irrational numbers
+aliases:
+  - Michael's product topology
 counterexamples_id: 85
 refs:
-  - zb: "0386.54001" 
+  - zb: "0386.54001"
     name: Counterexamples in Topology
 ---
 
diff --git a/spaces/S000077/properties/P000006.md b/spaces/S000077/properties/P000006.md
deleted file mode 100644
index a042eb8216..0000000000
--- a/spaces/S000077/properties/P000006.md
+++ /dev/null
@@ -1,7 +0,0 @@
----
-space: S000077
-property: P000006
-value: true
----
-
-Follows as this space is the product of {P000006} spaces.
diff --git a/spaces/S000077/properties/P000028.md b/spaces/S000077/properties/P000028.md
new file mode 100644
index 0000000000..fd82e6262b
--- /dev/null
+++ b/spaces/S000077/properties/P000028.md
@@ -0,0 +1,7 @@
+---
+space: S000077
+property: P000028
+value: true
+---
+
+{S63|P28} and {S28|P28}, hence so is their product.
diff --git a/spaces/S000077/properties/P000036.md b/spaces/S000077/properties/P000036.md
deleted file mode 100644
index 41f7b1dc48..0000000000
--- a/spaces/S000077/properties/P000036.md
+++ /dev/null
@@ -1,7 +0,0 @@
----
-space: S000077
-property: P000036
-value: false
----
-
-Follows as {S28|P36} and a product is connected if and only if its factors are connected.
diff --git a/spaces/S000077/properties/P000050.md b/spaces/S000077/properties/P000050.md
new file mode 100644
index 0000000000..48dc58cb6f
--- /dev/null
+++ b/spaces/S000077/properties/P000050.md
@@ -0,0 +1,7 @@
+---
+space: S000077
+property: P000050
+value: true
+---
+
+{S63|P50} and {S28|P50}, hence so is their product.
diff --git a/spaces/S000077/properties/P000051.md b/spaces/S000077/properties/P000051.md
deleted file mode 100644
index 906fc7ee27..0000000000
--- a/spaces/S000077/properties/P000051.md
+++ /dev/null
@@ -1,7 +0,0 @@
----
-space: S000077
-property: P000051
-value: false
----
-
-$X$ contains {S63} as a subspace and {S63|P51}.
diff --git a/spaces/S000077/properties/P000062.md b/spaces/S000077/properties/P000062.md
new file mode 100644
index 0000000000..3dbab885b8
--- /dev/null
+++ b/spaces/S000077/properties/P000062.md
@@ -0,0 +1,8 @@
+---
+space: S000077
+property: P000062
+value: false
+---
+
+If $X$ is {P62}, then so is each of its factors.
+However, {S63|P62}.
diff --git a/spaces/S000077/properties/P000063.md b/spaces/S000077/properties/P000063.md
new file mode 100644
index 0000000000..0e101d7647
--- /dev/null
+++ b/spaces/S000077/properties/P000063.md
@@ -0,0 +1,7 @@
+---
+space: S000077
+property: P000063
+value: false
+---
+
+$X$ contains {S63} as a closed subspace and {S63|P63}.
diff --git a/spaces/S000077/properties/P000065.md b/spaces/S000077/properties/P000065.md
deleted file mode 100644
index 7eb56f37ba..0000000000
--- a/spaces/S000077/properties/P000065.md
+++ /dev/null
@@ -1,7 +0,0 @@
----
-space: S000077
-property: P000065
-value: true
----
-
-By construction, as $\mathfrak c \cdot \mathfrak c = \mathfrak c$.
diff --git a/spaces/S000077/properties/P000139.md b/spaces/S000077/properties/P000139.md
new file mode 100644
index 0000000000..8d88a2a713
--- /dev/null
+++ b/spaces/S000077/properties/P000139.md
@@ -0,0 +1,8 @@
+---
+space: S000077
+property: P000139
+value: false
+---
+
+If $X$ {P139}, then so does each of its factors.
+However, {S28|P139}.
diff --git a/spaces/S000077/properties/P000166.md b/spaces/S000077/properties/P000166.md
new file mode 100644
index 0000000000..3e73ba027a
--- /dev/null
+++ b/spaces/S000077/properties/P000166.md
@@ -0,0 +1,7 @@
+---
+space: S000077
+property: P000166
+value: true
+---
+
+The Euclidean topology of $\mathbb R \times (\mathbb R \setminus \mathbb Q)$ is a coarser topology which is {P26} and {P53}.
diff --git a/spaces/S000077/properties/P000167.md b/spaces/S000077/properties/P000167.md
deleted file mode 100644
index 45ab185caa..0000000000
--- a/spaces/S000077/properties/P000167.md
+++ /dev/null
@@ -1,7 +0,0 @@
----
-space: S000077
-property: P000167
-value: false
----
-
-$X$ contains a copy of {S28} as a subspace and {S28|P167}.
diff --git a/spaces/S000077/properties/P000206.md b/spaces/S000077/properties/P000206.md
new file mode 100644
index 0000000000..2fb255b1e0
--- /dev/null
+++ b/spaces/S000077/properties/P000206.md
@@ -0,0 +1,7 @@
+---
+space: S000077
+property: P000206
+value: true
+---
+
+{S63|P206} and {S28|P206}, hence so is their product.