Typo fixes.
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@@ -5,7 +5,7 @@
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\label{definition:vanish-at-infinity}
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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.
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The set $C_0(X; \complex)$ is the space of all functions that vanish at infinity.
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The set $C_0(X; E)$ is the space of all functions that vanish at infinity.
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\end{definition}
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\begin{proposition}
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@@ -35,6 +35,6 @@
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\[
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(\phi f - f)(X) = \underbrace{(\phi f - f)(\bracs{f \not\in U})}_{0} + \underbrace{(\phi f - f)(\bracs{f \in U})}_{\in U} \in U
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\]
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so $f \in \ol{C_c(X; E)}$.
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\end{proof}
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