Theorem
Completeness is not a topological property preserved by homeomorphisms.
Proof
with the Euclidean metric is complete but
with the Euclidean metric is not.
is homeomorphic toso completeness is not a topological property.
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Theorem
Completeness is not a topological property preserved by homeomorphisms.
Proof
with the Euclidean metric is complete butwith the Euclidean metric is not.
is homeomorphic toso completeness is not a topological property.