diff --git a/properties/P000197.md b/properties/P000197.md
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--- /dev/null
+++ b/properties/P000197.md
@@ -0,0 +1,6 @@
+---
+uid: P000197
+name: Countable spread
+---
+
+A space in which every discrete subspace has countable cardinality.
diff --git a/properties/P000198.md b/properties/P000198.md
new file mode 100644
index 000000000..f5b0f3af9
--- /dev/null
+++ b/properties/P000198.md
@@ -0,0 +1,6 @@
+---
+uid: P000198
+name: Countable extent
+---
+
+A space in which every uncountable subspace has a limit point.
diff --git a/theorems/T000559.md b/theorems/T000559.md
new file mode 100644
index 000000000..d385122ac
--- /dev/null
+++ b/theorems/T000559.md
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+---
+uid: T000559
+if:
+  and:
+  - P000197: true
+  - P000052: true
+then:
+  P000057: true
+---
+
+Follows from the definition of {P197}.
\ No newline at end of file
diff --git a/theorems/T000560.md b/theorems/T000560.md
new file mode 100644
index 000000000..a339854dc
--- /dev/null
+++ b/theorems/T000560.md
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+---
+uid: T000560
+if:
+    P000131: true
+then:
+  P000197: true
+---
+
+Follows as Lindelöf discrete spaces are countable.
diff --git a/theorems/T000561.md b/theorems/T000561.md
new file mode 100644
index 000000000..3779eb651
--- /dev/null
+++ b/theorems/T000561.md
@@ -0,0 +1,9 @@
+---
+uid: T000561
+if:
+    P000180: true
+then:
+  P000197: true
+---
+
+Follows as separable discrete spaces are countable.
diff --git a/theorems/T000562.md b/theorems/T000562.md
new file mode 100644
index 000000000..5c91efd48
--- /dev/null
+++ b/theorems/T000562.md
@@ -0,0 +1,9 @@
+---
+uid: T000561
+if:
+    P000198: true
+then:
+  P000197: true
+---
+
+Follows as every uncountable subspace has a point that isn't isolated.