Typo fixes.

This commit is contained in:
Bokuan Li
2026-03-15 12:32:31 -04:00
parent f951ccccdf
commit 62a8e78dfe
3 changed files with 29 additions and 18 deletions

View File

@@ -5,7 +5,7 @@
\label{definition:vanish-at-infinity}
Let $X$ be a topological space, $E$ be a TVS over $K \in \RC$, and $f \in C(X; E)$, then $f$ \textbf{vanishes at infinity} if for every $U \in \cn_E^o(0)$, $\bracs{f \not\in U}$ is compact.
The set $C_0(X; \complex)$ is the space of all functions that vanish at infinity.
The set $C_0(X; E)$ is the space of all functions that vanish at infinity.
\end{definition}
\begin{proposition}
@@ -35,6 +35,6 @@
\[
(\phi f - f)(X) = \underbrace{(\phi f - f)(\bracs{f \not\in U})}_{0} + \underbrace{(\phi f - f)(\bracs{f \in U})}_{\in U} \in U
\]
so $f \in \ol{C_c(X; E)}$.
\end{proof}