Joint continuity of separately continuous functions
Joint continuity of separately continuous functions
It is shown that a separately continuous function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f colon upper X times upper Y right-arrow upper Z"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:mi>X</mml:mi> <mml:mo>×</mml:mo> <mml:mi>Y</mml:mi> <mml:mo stretchy="false">→</mml:mo> <mml:mi>Z</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">f:X \times Y \to Z</mml:annotation> </mml:semantics> </mml:math> </inline-formula> from the product of a certain type of …