Mathematics · Metric Spaces
Let (X, d) be a metric space. Then (X, d) is connected if and only if:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1there exists a proper subset of X that is both open and closed in X.
- 2there exist two non-empty disjoint open subsets A and B such that X = A ∪ B.
- 3there exists a continuous mapping of (X, d) onto a discrete metric space {0, 1}.
- 4the only continuous mappings of (X, d) into a discrete metric space {0, 1} are constant mappings.✓
Correct answer
the only continuous mappings of (X, d) into a discrete metric space {0, 1} are constant mappings.
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