Exercise · ZW-INTERIOR-OF-A-SET-001 · ★☆☆ Basic
In \(X=\{1,2,3\}\) with \(\mathcal{T}=\{\varnothing,\{1\},\{1,2\},\{1,2,3\}\}\), what is the interior of \(A=\{1,3\}\)?
Choose one option.
Show answer
- B. \(\{1\}\)
Explanation
The open sets contained in \(A\) are \(\varnothing\) and \(\{1\}\); the largest is \(\{1\}\).
Review the concept: Interior of a set
The interior \(\operatorname{int}A\) of a subset \(A\) of a topological space \((X,\mathcal{T})\) is the largest open set \(U\in\mathcal{T}\) contained in \(A\).
\[\operatorname{int}A=\bigcup\{U\in\mathcal{T}:\ U\subseteq A\}\]
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