Updated the uniform topology on function spaces.
This commit is contained in:
@@ -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 $X^T$.
|
||||
|
||||
Reference in New Issue
Block a user