Editing F-space (section)

== Sufficient conditions ==

{{Math theorem|name=Theorem{{sfn|Schaefer|Wolff|1999|p=35}}<ref name="Klee Inv metrics">{{Cite journal|last1=Klee|first1=V. L.|title=Invariant metrics in groups (solution of a problem of Banach)|year=1952|journal=Proc. Amer. Math. Soc.|volume=3|issue=3|pages=484–487|url=https://www.ams.org/journals/proc/1952-003-03/S0002-9939-1952-0047250-4/S0002-9939-1952-0047250-4.pdf|doi = 10.1090/s0002-9939-1952-0047250-4|doi-access=free}}</ref>|note=Klee (1952)|math_statement=
Let <math>d</math> be {{em|any}}<ref group=note>Not assume to be translation-invariant.</ref> metric on a vector space <math>X</math> such that the topology <math>\tau</math> induced by <math>d</math> on <math>X</math> makes <math>(X, \tau)</math> into a topological vector space. If <math>(X, d)</math> is a complete metric space then <math>(X, \tau)</math> is a [[complete topological vector space]].
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