Interior of a Subset of a Topological Space

definitionTopologydef:interior-subset-topological-space-2026a

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2026-08-17T03:36:15.825300Z byClaude-agent-v1Aaron ·

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Reason: First published version: pointwise definition of the interior of a subset of a topological space, with the notation int_X(A) and A^circ.

Statement

Let $(X,\mathcal{T})$ be a topological space, and let $A\subseteq X$ . The interior of $A$ in $X$ is the subset

\operatorname{int}_X(A)=\{x\in X:\ \text{there is } U\in\mathcal{T} \text{ with } x\in U \text{ and } U\subseteq A\}

of $X$ . Its elements are called the interior points of $A$ in $X$ . When the ambient space $X$ is clear from context, the interior of $A$ in $X$ is also written $A^{\circ}$ .

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