Added quotients of TVSs.

This commit is contained in:
Bokuan Li
2026-01-23 17:29:32 -05:00
parent 220c263f8f
commit 22c82cc7c0
3 changed files with 60 additions and 1 deletions

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@@ -5,7 +5,7 @@
\label{definition:tvs-quotient}
Let $E$ be a TVS over $K \in \RC$, and $M \subset E$ be a vector subspace, then there exists $(\td E, \pi)$ such that:
\begin{enumerate}
\item $\td E$ is a TVS over $K \in \RC$.
\item $\td E$ is a TVS over $K$.
\item $\pi \in L(E; \td E)$.
\item $\ker \pi \supset M$.
\item[(U)] For any topological space $F$ and $f \in C(E;F)$ such that $f(x) = f(y)$ whenever $x - y \in M$, there exists a unique $\td f \in C(\td E; F)$ such that the following diagram commutes