From d3f2b1be143808b7c289341f28ff6b608bc89009 Mon Sep 17 00:00:00 2001
From: Moniker1998 <88507423+Moniker1998@users.noreply.github.com>
Date: Mon, 7 Oct 2024 18:02:30 +0200
Subject: [PATCH] Weak topology on $\ell^2$ is an $\aleph_0$-space (#761)

* S21 has property P179

* fix upload-artifact

---------

Co-authored-by: Steven Clontz <steven.clontz@gmail.com>
---
 spaces/S000021/properties/P000179.md | 10 ++++++++++
 1 file changed, 10 insertions(+)
 create mode 100644 spaces/S000021/properties/P000179.md

diff --git a/spaces/S000021/properties/P000179.md b/spaces/S000021/properties/P000179.md
new file mode 100644
index 000000000..2f78bb788
--- /dev/null
+++ b/spaces/S000021/properties/P000179.md
@@ -0,0 +1,10 @@
+---
+space: S000021
+property: P000179
+value: true
+refs:
+- mr: 206907
+  name: $\aleph_0$-spaces (E. Michael)
+---
+Corollary 7.10 of {{mr:206907}} says that dual of a separable Banach space in its weak* topology is an $\aleph_0$-space. 
+Since $\ell^2$ is a separable Banach space with $\ell^2$ as its dual, the weak and weak* topology on $\ell^2$ coincide, and corollary 7.10 applies.