Definition:Topologically Complete

Definition

Let $T = \left({X, \vartheta}\right)$ be a topological space.

Let $M = \left({X, d}\right)$ be a complete metric space such that $\left({X, \vartheta}\right)$ is the topological space induced by $d$.

If there exists such a complete metric space, then $T$ is described as topologically complete.

Sources

• Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 5$: Complete Metric Spaces