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A note on identifications of metric spaces

A note on identifications of metric spaces

A space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is said to be <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma upper M upper K"> <mml:semantics> <mml:mrow> <mml:mi>σ<!-- σ --></mml:mi> <mml:mi>M</mml:mi> <mml:mi>K</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\sigma MK</mml:annotation> </mml:semantics> </mml:math> </inline-formula> provided that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> …