Mathematics · Topology
Which topology on a set X is called the metric topology induced by a metric d?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The topology generated by the collection {(x d , ε) x, ε > 0}
- 2The topology generated by the collection {(x d , ε) | x, ε > 0}
- 3The topology generated by the collection of all open balls {B d (x, ε) | x ∈ X, ε > 0}✓
- 4The topology generated by the collection {B(x, ε) | x ∈ X, ε > 0}
Correct answer
The topology generated by the collection of all open balls {B d (x, ε) | x ∈ X, ε > 0}
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