Exercise · ZW-INTERIOR-OF-A-SET-008 · ★★☆ Intermediate
In \(X=\{1,2,3,4\}\) with \(\mathcal{T}=\{\varnothing,\{1\},\{3\},\{1,3\},\{1,2,3\},\{1,3,4\},\{1,2,3,4\}\}\), for which of these sets \(A\) does \(\operatorname{int}A=A\) hold?
Choose one option.
A \(\{1,3,4\}\) B \(\{1,2\}\) C \(\{2,3\}\) D \(\{3,4\}\) Show answer ← Back to the question
Explanation \(\operatorname{int}A=A\) means \(A\) is open, and \(\{1,3,4\}\) is the only one in the list that belongs to \(\mathcal{T}\).
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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