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Added the existence of projections.
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Bokuan Li
2026-08-09 15:40:56 -04:00
parent 1bc1b17fee
commit 575cd66ad8
6 changed files with 116 additions and 5 deletions
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src/fa/order/order.tex
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@@ -54,3 +54,9 @@
\label{definition:order-vector-complete}
Let $(E, \le)$ be an ordered vector space, then $E$ is \textbf{order complete} if for any order bounded set $A \subset E$, $\sup (A)$ and $\inf (A)$ exist.
\end{definition}
\begin{definition}[Monotone Complete]
\label{definition:monotone-complete}
Let $(E, \le)$ be an ordered vector space, then $E$ is \textbf{monotone complete} if for any order bounded directed set $A \subset E$, $\sup(A)$ exists.
\end{definition}