A characterization of metric completeness
A characterization of metric completeness
A proof is given of a theorem, relevant to fixed-point theory, which implies that a metric space (<italic>X, d</italic>) is complete if and only if, for each continuous function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="h colon upper X right-arrow bold upper R"> <mml:semantics> <mml:mrow> <mml:mi>h</mml:mi> <mml:mo>:</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">→<!-- → --></mml:mo> …