On ideals consisting of joint topological divisors of zero
Zbigniew Słodkowski (1973)
Studia Mathematica
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Zbigniew Słodkowski (1973)
Studia Mathematica
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Donald Plank (1969)
Fundamenta Mathematicae
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Z. Semadeni (1963)
Fundamenta Mathematicae
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Jorma Arhippainen (1992)
Studia Mathematica
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Let X be a completely regular topological space and A a commutative locally m-convex algebra. We give a description of all closed and in particular closed maximal ideals of the algebra C(X,A) (= all continuous A-valued functions defined on X). The topology on C(X,A) is defined by a certain family of seminorms. The compact-open topology of C(X,A) is a special case of this topology.
David A. Rose, T. R. Hamlett (1992)
Mathematica Slovaca
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Leonard Yap (1970)
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Detlev Poguntke (1996)
Colloquium Mathematicae
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William Dietrich (1975)
Fundamenta Mathematicae
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Sławomir Solecki (2001)
Fundamenta Mathematicae
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We study the σ-ideal of Haar null sets on Polish groups. It is shown that on a non-locally compact Polish group with an invariant metric this σ-ideal is closely related, in a precise sense, to the σ-ideal of non-dominating subsets of . Among other consequences, this result implies that the family of closed Haar null sets on a Polish group with an invariant metric is Borel in the Effros Borel structure if, and only if, the group is locally compact. This answers a question of Kechris....