jerrylicious/garden
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Added the compact null sequence lemma.

Browse Source
This commit is contained in:
Bokuan Li
2026-07-17 14:29:04 -04:00
parent fe557de4a6
commit 843631b024
3 changed files with 56 additions and 2 deletions
Download Patch File Download Diff File Expand all files Collapse all files

2
src/fa/lc/tensor.tex
View File

@@ -28,7 +28,7 @@
The space $E \otimes_\pi F$ is the \textbf{projective tensor product} of $E$ and $F$, and the mapping $\iota \in L^2(E, F; E \otimes_\pi F)$ is the \textbf{canonical embedding}.
The space $E \widetilde{\otimes}_\pi F$ denotes the Hausdorff completion of $E \otimes_\pi F$.
The space $E \wh{\otimes}_\pi F$ denotes the Hausdorff completion of $E \otimes_\pi F$.
\end{definition}
\begin{proof}
Let $E \otimes_\pi F = E \otimes F$ be the \hyperref[tensor product]{definition:tensor-product} of $E$ and $F$ as vector spaces. Let $\mathscr{T} \subset 2^{2^X}$ be the collection of all locally convex topologies satisfying (1) and (2), and let $\mathcal{S}$ be the projective topology on $E \otimes_\pi F$ generated by $\mathscr{T}$.