image of a subset under a function

像

Foundations & Logic · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: direct image

Translation evidence: Literature usage

Meaning in context

For f:A→B and S⊆A, the set of values f(s) for s∈S.

对于 f:A→B 和 S⊆A，所有 f(s)（s∈S）构成的集合。

Example

For f(n)=n2f(n)=n^2, f[{−2,2}]={4}f[\{-2,2\}]=\{4\}.

Usage and distinctions

Images preserve unions but need not preserve intersections when f is not injective.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§15.1 The Function Concept; §15.2 Injective, Surjective, and Bijective Functions; §15.3 Functions and Subsets of the Domain · Checked 2026-10-14

Translation sources

  1. 鲍志强（北京大学）— 拓扑学2007年秋季教学纲要第1周9月12日，主要概念：「像」 · Checked 2026-10-14
Edit source / propose a PRReport a correction

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.