From badf8ad48666cc6b82d858f701d431d3992bc71a Mon Sep 17 00:00:00 2001
From: Bokuan Li <47512608+Jerry-licious@users.noreply.github.com>
Date: Mon, 5 Jan 2026 20:18:26 -0500
Subject: [PATCH] Updated the uniform topology on function spaces.

---
 src/topology/functions/set-systems.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/topology/functions/set-systems.tex b/src/topology/functions/set-systems.tex
index 26369cc..a9aa501 100644
--- a/src/topology/functions/set-systems.tex
+++ b/src/topology/functions/set-systems.tex
@@ -33,7 +33,7 @@
         \item The topology induced by $\fV$ is finer than the $\mathfrak{S}$-topology on $T^X$.
         \item If $\mathfrak{S}$ is upward-directed with respect to inclusion, then $\mathfrak{E}(\mathfrak{S}, \fU)$ is forms a fundamental system of entourages for $\fV$.
     \end{enumerate}
-    and the topology induced by $\fV$ is the \textbf{topology of uniform convergence on the sets $\mathfrak{S}$}, or the $\mathfrak{S}$-topology.
+    and the topology induced by $\fV$ is the \textbf{topology of uniform convergence on the sets $\mathfrak{S}$}/\textbf{$\mathfrak{S}$-uniform topology} on $X^T$.
 \end{definition}
 \begin{proof}
     (1): Since $\Delta \subset E(S, U)$ for all $S \in \mathfrak{S}$ and $U \in \fU$, $\mathfrak{E}(\mathfrak{S}, \fU)$ generates a uniformity on $X^T$.