Last modified date: <%+ tp.file.last_modified_date() %>
- Tags:
- Refs:
- Links:
universally closed
-
A morphism \(f: X\to Y\) is universally closed iff the following is a closed map for all \(Z\):
\begin{align*}
X\times Z\xrightarrow{(f, \operatorname{id}_Z)} Y\times Z
\end{align*}
- Equivalently when \(Y\) is Hausdorff: for any map \(Z\to Y\), the following pullback is a closed map: \begin{align*} X \underset{\scriptscriptstyle {Y} }{\times} Z\to Z \end{align*}
- For \(X\) Hausdorff and \(Y\) locally compact, \(f:X\to Y\) is universally closed iff \(f\) is proper.
