diff --git a/properties/P000182.md b/properties/P000182.md
index ce106f24c3..ca1c62398d 100644
--- a/properties/P000182.md
+++ b/properties/P000182.md
@@ -16,3 +16,4 @@ Defined on page 127 of {{zb:0684.54001}}.
 ### Meta-properties
 
 - This property is hereditary.
+- This property is preserved by countable products.
diff --git a/properties/P000183.md b/properties/P000183.md
index 7b97dc0ae2..be2f6283f7 100644
--- a/properties/P000183.md
+++ b/properties/P000183.md
@@ -6,16 +6,33 @@ refs:
     name: $\aleph_0$-spaces (E. Michael)
   - doi: 10.1016/j.topol.2015.05.085
     name: $\mathfrak P$-spaces and related concepts (Gabriyelyan & Kakol)
+  - mo: 495213
+    name: Product of spaces with countable $k$-networks
+  - mo: 506308
+    name: Answer to "Product of spaces with countable $k$-networks"
 ---
 
 A space with a (finite or infinite) countable $k$-network.
 
-Equivalently, a space with a countable pseudobase.
+Equivalently:
+1. A space with countable pseudobase.
+2. A space with countable $cs$-network.
+3. A space with countable $cs^\ast$-network.
 
 A family $\mathcal N$ of subsets of $X$ is called a *$k$-network* if for every compact set $K$ and open set $U$ in $X$ with $K\subseteq U$, there exists a finite $\mathcal{N}^* \subseteq \mathcal{N}$ with $K \subseteq \bigcup\mathcal{N}^* \subseteq U$.
 
-And a family $\mathcal{N}$ of subsets of $X$ is called a *pseudobase* if for every compact set $K$ and open set $U$ in $X$ with $K\subseteq U$, there exists some $A\in\mathcal{N}$ with $K \subseteq A \subseteq U$.
+A family $\mathcal{N}$ of subsets of $X$ is called a *pseudobase* if for every compact set $K$ and open set $U$ in $X$ with $K\subseteq U$, there exists some $A\in\mathcal{N}$ with $K \subseteq A \subseteq U$.
 
-For the equivalence between the two characterizations, note that every pseudobase is a $k$-network.  And conversely given a countable $k$-network $\mathcal N$, the collection of finite unions of elements of $\mathcal N$ is a countable pseudobase.
+A family $\mathcal{N}$ of subsets of $X$ is called a *$cs$-network* if for every sequence $x_n$ convergent to $x$ and open set $U$ in $X$ with $x\in U$, there exists some $A\in\mathcal{N}$ with $x_n\in A$ for all but finitely many $n$.
+
+A family $\mathcal{N}$ of subsets of $X$ is called a *$cs^\ast$-network* if for every sequence $x_n$ convergent to $x$ and open set $U$ in $X$ with $x\in U$, there exists some $A\in\mathcal{N}$ with $x_n\in A$ for infinitely many $n$.
+
+To see the equivalence, first note that a pseudobase is a $k$-network, a $k$-network is a $cs$-network and a $cs$-network is a $cs^\ast$-network. In {{mo:506308}} it is shown that if $X$ has countable $cs^\ast$-network, then it has a countable $k$-network. Then finite unions of elements of that $k$-network form a countable pseudobase.
 
 See {{mr:206907}}, available at <https://www.jstor.org/stable/24901448>.
+
+---
+### Meta-properties
+
+- This property is preserved by countable products. (see {{mo:495213}})
+
diff --git a/spaces/S000031/properties/P000183.md b/spaces/S000031/properties/P000183.md
new file mode 100644
index 0000000000..098c809295
--- /dev/null
+++ b/spaces/S000031/properties/P000183.md
@@ -0,0 +1,7 @@
+---
+space: S000031
+property: P000183
+value: true
+---
+
+$X$ is a square of {S29} and {S29|P183}.