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Complete metric space

Ciro Santilli (@cirosantilli, 37) ... Mathematics Area of mathematics Calculus Topology Metric (mathematics) Metric space
Updated 2025-07-16  1 By others on same topic  0 Discussions Create my own version
In plain English: the space has no visible holes. If you start walking less and less on each step, you always converge to something that also falls in the space.
One notable example where completeness matters: Lebesgue integral of Lp is complete but Riemann isn't.

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  • Lebesgue integral of Lp is complete but Riemann isn't

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Complete metric space by Wikipedia Bot 0
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A **complete metric space** is a type of metric space that possesses a specific property: every Cauchy sequence in that space converges to a limit that is also within the same space. To break this down: 1. **Metric Space**: A metric space is a set \(X\) along with a metric (or distance function) \(d: X \times X \to \mathbb{R}\).
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