Mathematics · Topology and Metric Spaces
Let (X, d) be a metric space. A subset A ⊆ X is open if and only if:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1A contains all its boundary points.
- 2A = cl(A).
- 3For each x ∈ A, there exists r > 0 such that B(x, r) ⊆ A.✓
- 4It contains all its limit points.
Correct answer
For each x ∈ A, there exists r > 0 such that B(x, r) ⊆ A.
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