Notation 2.4.4.1.2 (007H): Further Notation for Direct Images

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Table of Contents
Part 1: Sets
Chapter 2: Constructions With Sets
Section 2.4: Powersets
Subsection 2.4.4: Direct Images
Notation 2.4.4.1.2: Further Notation for Direct Images (cite)

Notation 2.4.4.1.2 ▶ Further Notation for Direct Images

Sometimes one finds the notation

\[ \exists _{f}\colon \mathcal{P}\webleft (A\webright )\to \mathcal{P}\webleft (B\webright ) \]

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

We have $b\in \exists _{f}\webleft (U\webright )$.
There exists some $a\in U$ such that $f\webleft (a\webright )=b$.

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