jerrylicious/garden
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Me when I forget to commit.

Browse Source
This commit is contained in:
Bokuan Li
2026-01-17 23:11:19 -05:00
parent af924f6225
commit 307f23ad57
23 changed files with 751 additions and 182 deletions
Download Patch File Download Diff File Expand all files Collapse all files

4
src/fa/tvs/bounded.tex
View File

@@ -3,12 +3,12 @@
\begin{definition}[Bounded]
\label{definition:bounded}
Let $E$ be a TVS over $K \in \RC$ and $B \subset E$, then $B$ is \textbf{bounded} if for every $U \in \cn(0)$, there exists $\lambda \in K$ such that $\lambda U \supset B$.
Let $E$ be a TVS over $K \in \RC$ and $B \subset E$, then $B$ is \textbf{bounded} if for every $U \in \cn(0)$, there exists $\lambda \in K$ such that $\lambda U \supset B$. The collection $B(E)$ is the set of all bounded sets of $E$.
\end{definition}
\begin{proposition}[{{\cite[1.5.1]{SchaeferWolff}}}]
\label{proposition:bounded-operations}
Let $E$ be a TVS over $K \in \RC$ and $A, B \subset E$ be bounded, then the following sets are bounded:
Let $E$ be a TVS over $K \in \RC$ and $A, B \in B(E)$, then the following sets are bounded:
\begin{enumerate}
\item Any $C \subset B$.
\item The closure $\ol{B}$.