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@@ -95,7 +95,7 @@
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\end{proof}
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\begin{proposition}[{{\cite[I.1.1]{SchaeferWolff}}}]
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\begin{proposition}
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\label{proposition:tvs-set-operations}
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Let $G$ be a topological group and $A, B \subset G$, then
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\begin{enumerate}
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@@ -103,7 +103,7 @@
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\item If $A$ is closed and $B$ is compact, then $AB$ is closed.
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\end{enumerate}
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\end{proposition}
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\begin{proof}
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\begin{proof}[Proof, {{\cite[I.1.1]{SchaeferWolff}}}. ]
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(1): For every $x \in B$, $Ab$ is open by translation invariance, so
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\[
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AB = \bigcup_{x \in B}(Ab)
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@@ -122,7 +122,7 @@
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y \in \bigcap_{U \in \fF}\overline{UB^{-1}} \subset \bigcap_{U \in \fF}[UUB^{-1}]
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\]
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Since $\fF$ converges to $x$, (TVS1) implies that $\bracs{U + U| U \in \fF}$ contains a neighbourhood base of $x$. Thus
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Since $\fF$ converges to $x$, (TG1) implies that $\bracs{UU| U \in \fF}$ contains a neighbourhood base of $x$. Thus
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\[
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y \in \bigcap_{U \in \fF}[UUB^{-1}] \subset \bigcap_{V \in \cn_G(1)}[xVB^{-1}] = \overline{xB^{-1}} = xB^{-1}
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\]
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