Added bornological spaces.

This commit is contained in:
Bokuan Li
2026-05-02 15:59:03 -04:00
parent dcf11fb978
commit 1e53581113
8 changed files with 82 additions and 22 deletions

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@@ -111,7 +111,7 @@
\end{enumerate}
\end{theorem}
\begin{proof}
Suppose that $T(E)$ is not meagre. Let $r_0 > 0$ and $r > 0$ such that $B_E(0, r) + B_E(0, r) \subset B_E(0, r_0)$, then since $B_E(0, r)$ is absorbing,
Suppose that $T(E)$ is not meagre. Let $r_0 > 0$ and $r > 0$ such that $B_E(0, r) + B_E(0, r) \subset B_E(0, r_0)$, then since $B_E(0, r)$ is radial,
\[
E = \bigcup_{n \in \natp}nB_E(0, r) \quad \overline{T(E)} = \bigcup_{n \in \natp}\overline{nT(B_E(0, r))}
\]