Metrizable Space
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A Metrizable Space is a topological space that is homeomorphic to a metric space.
- See: Metric (Mathematics), Sufficient Condition, Topology, Mathematics, Topological Space, Homeomorphism, Metric Space, Pearson PLC, Theorem.
References
2024
- (Wikipedia, 2024) ⇒ https://en.wikipedia.org/wiki/Metrizable_space Retrieved:2024-9-2.
- In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space. That is, a topological space [math]\displaystyle{ (X, \tau) }[/math] is said to be metrizable if there is a metric [math]\displaystyle{ d : X \times X \to [0, \infty) }[/math] such that the topology induced by [math]\displaystyle{ d }[/math] is [math]\displaystyle{ \tau. }[/math] Metrization theorems are theorems that give sufficient conditions for a topological space to be metrizable.