The class of compact* spaces is productive and closed hereditary
The class of compact* spaces is productive and closed hereditary
W. W. Comfort defined compact<inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="Superscript asterisk"> <mml:semantics> <mml:msup> <mml:mi /> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> <mml:annotation encoding="application/x-tex">^ \ast</mml:annotation> </mml:semantics> </mml:math> </inline-formula> spaces as completely regular Hausdorff spaces <italic>X</italic> such that each maximal ideal in the ring <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Superscript asterisk Baseline left-parenthesis upper …