add and delete traits of four spaces

pi-base · Apr 1, 2024 · 42acc40 · 42acc40
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diff --git a/spaces/S000005/README.md b/spaces/S000005/README.md
@@ -8,7 +8,7 @@ refs:
   - wikipedia: Partition_topology
     name: Partition topology on Wikipedia
 ---
-Define a topology on $\mathbb{N}$ by taking as a basis all sets of the form $\{\{2k-1,2k\}\, |\, k \in \mathbb{N}\}$.
+Define a topology on $\mathbb{N}$ by taking as a basis all sets of the form $\{\{2k-1,2k\}\mid k \in \mathbb{N}\}$.
 
 Defined as counterexample #6 ("Odd-Even Topology")
 in {{doi:10.1007/978-1-4612-6290-9}}.

diff --git a/spaces/S000005/properties/P000050.md b/spaces/S000005/properties/P000050.md
diff --git a/spaces/S000005/properties/P000090.md b/spaces/S000005/properties/P000090.md
diff --git a/spaces/S000005/properties/P000185.md b/spaces/S000005/properties/P000185.md
@@ -0,0 +1,12 @@
+---
+space: S000005
+property: P000185
+value: true
+refs:
+- doi: 10.1007/978-1-4612-6290-9
+  name: Counterexamples in Topology
+---
+
+The basis $\{\{2k-1,2k\}\mid k \in \mathbb{N}\}$ is a partition.
+
+See the entry for space #6 in {{doi:10.1007/978-1-4612-6290-9}}.
diff --git a/spaces/S000006/properties/P000049.md b/spaces/S000006/properties/P000049.md
diff --git a/spaces/S000006/properties/P000090.md b/spaces/S000006/properties/P000090.md
diff --git a/spaces/S000006/properties/P000121.md b/spaces/S000006/properties/P000121.md
diff --git a/spaces/S000006/properties/P000185.md b/spaces/S000006/properties/P000185.md
@@ -0,0 +1,12 @@
+---
+space: S000005
+property: P000185
+value: true
+refs:
+- doi: 10.1007/978-1-4612-6290-9
+  name: Counterexamples in Topology
+---
+
+The basis $\{(n,n+1)\mid n \in \mathbb{Z}\}$ is a partition.
+
+See the entry for space #7 in {{doi:10.1007/978-1-4612-6290-9}}.
diff --git a/spaces/S000164/properties/P000078.md b/spaces/S000164/properties/P000078.md
diff --git a/spaces/S000164/properties/P000185.md b/spaces/S000164/properties/P000185.md
@@ -0,0 +1,7 @@
+---
+space: S000164
+property: P000185
+value: true
+---
+
+The basis $\{\{a,b\},\{c\}\}$ is a partition.
diff --git a/spaces/S000184/properties/P000086.md b/spaces/S000184/properties/P000086.md
@@ -0,0 +1,7 @@
+---
+space: S000184
+property: P000086
+value: true
+---
+
+{S184} is the product of two {P86} spaces; see {S1|P86} and {S4|P86}.
diff --git a/spaces/S000184/properties/P000125.md → spaces/S000184/properties/P000176.md b/spaces/S000184/properties/P000125.md → spaces/S000184/properties/P000176.md
@@ -1,6 +1,6 @@
 ---
 space: S000184
-property: P000125
+property: P000176
 value: true
 ---
 

diff --git a/spaces/S000184/properties/P000185.md b/spaces/S000184/properties/P000185.md
@@ -0,0 +1,7 @@
+---
+space: S000184
+property: P000185
+value: true
+---
+
+The basis $\{\{0,1\},\{2,3\}\}$ is a partition.