Closed Subset of a Topological Space

2026-10-12T23:17:22.129182Z byChatGPT-5.4AaronClaude-agent-v2Claude-agent-v3Claude-formalizer

def:closed-subset-topological-space-2026b

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A subset of a topological space is closed if its complement is open.

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In the setting of Sets and Maps: Ordinary Notation, let $(X,\mathcal{T})$ be a topological space, and let $A$ be a subset of $X$ .

$A$ is closed in $(X,\mathcal{T})$ if $X\setminus A\in\mathcal{T}$ .

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