Topological Completeness is Weakly Hereditary
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Theorem
Let $T = \left({X, \vartheta}\right)$ be a topological space which is topologically complete.
Let $V \subseteq X$ be a closed subspace of $T$.
Then $V$ is also topologically complete.
Proof
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Sources
- Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 5$: Complete Metric Spaces
