Added pseudonorms for TVSs.

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Bokuan Li
2026-01-24 17:35:48 -05:00
parent 514afcb21f
commit 008af3c2b8
6 changed files with 185 additions and 0 deletions

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@@ -146,6 +146,7 @@ The axioms of uniform spaces strongly resembles working in a metric space. In fa
\end{remark}
\begin{remark}
\label{remark:uniform-sequence-pseudometric}
It may be tempting to construct the level sets of the pseudometric on the dyadic rational numbers by composing these sets, then proceed to construct the pseudometric as in Urysohn's lemma. However, this approach has a major shortcoming in that the composition of symmetric entourages are not necessarily symmetric. As such, it is difficult to construct symmetric level sets for the desired pseudometric.
\end{remark}