Added universality of the zero-dimensional spaces.
This commit is contained in:
@@ -135,7 +135,7 @@
|
||||
\label{definition:seminorm-topology}
|
||||
Let $E$ be a vector space over $K \in \RC$ and $\seqi{[\cdot]}$ be seminorms, then:
|
||||
\begin{enumerate}
|
||||
\item For each $i \in I$, $d_i: E \times E \to [0, \infty)$ defined by $(x, y) \mapsto [x - y]_i$ is a pseudo-metric.
|
||||
\item For each $i \in I$, $d_i: E \times E \to [0, \infty)$ defined by $(x, y) \mapsto [x - y]_i$ is a pseudometric.
|
||||
\item The topology induced by $\seqi{d}$ makes $E$ a topological vector space.
|
||||
\item For each $i \in I$, $[\cdot]_i: E \to [0, \infty)$ is continuous.
|
||||
\end{enumerate}
|
||||
|
||||
Reference in New Issue
Block a user