Almost discrete implies hereditarily paracompact (#1429)

Moniker1998 · web-flow · commit c8ad47d5f547 · 2025-09-05T23:16:09.000-04:00
diff --git a/theorems/T000778.md b/theorems/T000778.md
@@ -0,0 +1,9 @@
+---
+uid: T000778
+if:
+  P000203: true
+then:
+  P000216: true
+---
+
+Any subspace of a {P203} space is {P203} or {P52}. Since [almost discrete spaces are paracompact](https://topology.pi-base.org/spaces?q=almost+discrete+%2B+not+paracompact) and [discrete spaces are paracompact](https://topology.pi-base.org/spaces?q=discrete+%2B+not+paracompact), it follows that any subspace of a {P203} space is {P30}.
