Exercise · ZW-INTERIOR-OF-A-SET-005 · ★★☆ Intermediate
In \(X=\{a,b,c\}\) with \(\mathcal{T}=\{\varnothing,\{a,b,c\}\}\), what is the interior of \(A=\{a,b\}\)?
Choose one option.
Show answer
- D. \(\varnothing\)
Explanation
In the trivial topology the only open sets are \(\varnothing\) and \(X\), and \(X\not\subseteq A\); the interior is \(\varnothing\).
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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