Exercise · ZW-INTERIOR-OF-A-SET-003 · ★☆☆ Basic
In \(X=\{a,b,c,d\}\) with \(\mathcal{T}=\{\varnothing,\{a\},\{b\},\{a,b\},\{a,b,c\},\{a,b,c,d\}\}\), what is the interior of \(A=\{a,b,d\}\)?
Choose one option.
Show answer
- C. \(\{a,b\}\)
Explanation
The open sets contained in \(A\) are \(\varnothing,\{a\},\{b\},\{a,b\}\); their union is \(\{a,b\}\).
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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