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 $X^T$.