Definition:Topologically Complete Space
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This page is about Topologically Complete Space. For other uses, see Complete.
Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $M = \struct {S, d}$ be a complete metric space such that $\struct {S, \tau}$ is the topological space induced by $d$.
If there exists such a complete metric space, then $T$ is described as topologically complete.
Also see
- Results about Topologically Complete Spaces can be found here.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $5$: Metric Spaces: Complete Metric Spaces