Exercise · ZW-INTERIOR-OF-A-SET-006 · ★★☆ Intermediate
In \(X=\{a,b,c,d\}\) with \(\mathcal{T}=\{\varnothing,\{a\},\{b\},\{a,b\},\{a,b,c\},\{a,b,c,d\}\}\), how many elements does the interior of \(A=\{a,c,d\}\) have?
Choose one option.
A 0 B 1 C 2 D 3 Show answer ← Back to the question
Explanation The only nonempty open set inside \(A\) is \(\{a\}\), so the interior has one element.
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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