Metrizable Space

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.

---