From 442d732696ad431b84f6e5c72b6ee785be4fd968 Mon Sep 17 00:00:00 2001
From: adelon <22380201+adelon@users.noreply.github.com>
Date: Sat, 10 Feb 2024 02:22:14 +0100
Subject: Initial commit

---
 library/topology/preclosure.tex | 18 ++++++++++++++++++
 1 file changed, 18 insertions(+)
 create mode 100644 library/topology/preclosure.tex

(limited to 'library/topology/preclosure.tex')

diff --git a/library/topology/preclosure.tex b/library/topology/preclosure.tex
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+++ b/library/topology/preclosure.tex
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+\import{set.tex}
+
+\section{Preclosure spaces}
+
+
+\begin{struct}
+    A preclosure space $X$ is a onesorted structure equipped with
+    \begin{enumerate}
+        \item $\cl$
+    \end{enumerate}
+    such that
+    \begin{enumerate}
+        \item For all $Y\subseteq X$ we have $\cl(Y)\subseteq X$.
+        \item $\cl(\emptyset) = \emptyset$.
+        \item For all $A$ we have $A\subseteq \cl(A)$.
+        \item For all $A, B$ we have $\cl(A\union B) = \cl(A) \union \cl(B)$.
+    \end{enumerate}
+\end{struct}
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