Topological Completeness is a Topological Property
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Theorem
Let $T_A = \left({A, \vartheta_A}\right)$ and $T_B = \left({B, \vartheta_B}\right)$ be topological spaces which are homeomorphic.
Let $T_A$ be topologically complete.
Then $T_B$ 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
