Notation 2.6.3.1.2 (008K): Further Notation for Direct Images With Compact Support

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Table of Contents
Part 1: Sets
Chapter 2: Constructions With Sets
Section 2.6: The Adjoint Triple $f_{*}\dashv f^{-1}\dashv f_{!}$
Subsection 2.6.3: Direct Images With Compact Support
Notation 2.6.3.1.2: Further Notation for Direct Images With Compact Support (cite)

Notation 2.6.3.1.2 ▶ Further Notation for Direct Images With Compact Support

Sometimes one finds the notation

\[ \forall _{f}\colon \mathcal{P}\webleft (X\webright )\to \mathcal{P}\webleft (Y\webright ) \]

for $f_{*}$. This notation comes from the fact that the following statements are equivalent, where $y\in Y$ and $U\in \mathcal{P}\webleft (X\webright )$:

We have $y\in \forall _{f}\webleft (U\webright )$.
For each $x\in X$, if $y=f\webleft (x\webright )$, then $x\in U$.

We will not make use of this notation in the present work.

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