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• W1978478535 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper P Subscript k Baseline left-parenthesis upper X right-parenthesis> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>{P_k}left ( X right )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denote the set of all probability measures on a metric 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> whose supports consist of no more than <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> points, equipped with the Fedorchuk topology. We prove that if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X element-of ANR> <mml:semantics> <mml:mrow> <mml:mi>X</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mtext>ANR</mml:mtext> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>X in {text {ANR}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> then <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper P Subscript k Baseline left-parenthesis upper X right-parenthesis element-of ANR> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mtext>ANR</mml:mtext> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>{P_k}left ( X right ) in {text {ANR}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for every <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k element-of bold upper N> <mml:semantics> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=bold>N</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>k in {mathbf {N}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. This implies that for each <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k element-of bold upper N> <mml:semantics> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=bold>N</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>k in {mathbf {N}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> the functor <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper P Subscript k> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{P_k}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> preserves the topology of separable Hilbert space." @default.
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• W1978478535 date "1989-01-01" @default.
• W1978478535 modified "2023-09-26" @default.
• W1978478535 title "Probability measure functors preserving the ANR-property of metric spaces" @default.
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• W1978478535 doi "https://doi.org/10.1090/s0002-9939-1989-0964459-9" @default.
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