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A mapping theorem for Hilbert cube manifolds
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Zeitschriftentitel: | Proceedings of the American Mathematical Society |
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Personen und Körperschaften: | |
In: | Proceedings of the American Mathematical Society, 88, 1983, 1, S. 165-168 |
Format: | E-Article |
Sprache: | Englisch |
veröffentlicht: |
American Mathematical Society (AMS)
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Schlagwörter: |
author_facet |
Prasad, V. S. Prasad, V. S. |
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author |
Prasad, V. S. |
spellingShingle |
Prasad, V. S. Proceedings of the American Mathematical Society A mapping theorem for Hilbert cube manifolds Applied Mathematics General Mathematics |
author_sort |
prasad, v. s. |
spelling |
Prasad, V. S. 0002-9939 1088-6826 American Mathematical Society (AMS) Applied Mathematics General Mathematics http://dx.doi.org/10.1090/s0002-9939-1983-0691301-0 <p>We show that every compact connected Hilbert cube manifold <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> can be obtained from the Hilbert cube <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Q"> <mml:semantics> <mml:mi>Q</mml:mi> <mml:annotation encoding="application/x-tex">Q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> by making identifications on a face of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Q"> <mml:semantics> <mml:mi>Q</mml:mi> <mml:annotation encoding="application/x-tex">Q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Some applications of this result to measure preserving homeomorphisms on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are given: (1) The first is concerned with which measures on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are equivalent to each other by homeomorphisms. (2) The second application is about approximating invertible Borel measurable transformations of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> by measure preserving homeomorphisms of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. (3) The final application is concerned with generic properties of measure preserving homeomorphisms of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p> A mapping theorem for Hilbert cube manifolds Proceedings of the American Mathematical Society |
doi_str_mv |
10.1090/s0002-9939-1983-0691301-0 |
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Online Free |
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Mathematik |
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ElectronicArticle |
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imprint |
American Mathematical Society (AMS), 1983 |
imprint_str_mv |
American Mathematical Society (AMS), 1983 |
issn |
0002-9939 1088-6826 |
issn_str_mv |
0002-9939 1088-6826 |
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English |
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publishDateSort |
1983 |
publisher |
American Mathematical Society (AMS) |
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ai |
record_format |
ai |
series |
Proceedings of the American Mathematical Society |
source_id |
49 |
title |
A mapping theorem for Hilbert cube manifolds |
title_unstemmed |
A mapping theorem for Hilbert cube manifolds |
title_full |
A mapping theorem for Hilbert cube manifolds |
title_fullStr |
A mapping theorem for Hilbert cube manifolds |
title_full_unstemmed |
A mapping theorem for Hilbert cube manifolds |
title_short |
A mapping theorem for Hilbert cube manifolds |
title_sort |
a mapping theorem for hilbert cube manifolds |
topic |
Applied Mathematics General Mathematics |
url |
http://dx.doi.org/10.1090/s0002-9939-1983-0691301-0 |
publishDate |
1983 |
physical |
165-168 |
description |
<p>We show that every compact connected Hilbert cube manifold <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M">
<mml:semantics>
<mml:mi>M</mml:mi>
<mml:annotation encoding="application/x-tex">M</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula> can be obtained from the Hilbert cube <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Q">
<mml:semantics>
<mml:mi>Q</mml:mi>
<mml:annotation encoding="application/x-tex">Q</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula> by making identifications on a face of <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Q">
<mml:semantics>
<mml:mi>Q</mml:mi>
<mml:annotation encoding="application/x-tex">Q</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>. Some applications of this result to measure preserving homeomorphisms on <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M">
<mml:semantics>
<mml:mi>M</mml:mi>
<mml:annotation encoding="application/x-tex">M</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula> are given: (1) The first is concerned with which measures on <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M">
<mml:semantics>
<mml:mi>M</mml:mi>
<mml:annotation encoding="application/x-tex">M</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula> are equivalent to each other by homeomorphisms. (2) The second application is about approximating invertible Borel measurable transformations of <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M">
<mml:semantics>
<mml:mi>M</mml:mi>
<mml:annotation encoding="application/x-tex">M</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula> by measure preserving homeomorphisms of <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M">
<mml:semantics>
<mml:mi>M</mml:mi>
<mml:annotation encoding="application/x-tex">M</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>. (3) The final application is concerned with generic properties of measure preserving homeomorphisms of <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M">
<mml:semantics>
<mml:mi>M</mml:mi>
<mml:annotation encoding="application/x-tex">M</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>.</p> |
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description | <p>We show that every compact connected Hilbert cube manifold <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> can be obtained from the Hilbert cube <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Q"> <mml:semantics> <mml:mi>Q</mml:mi> <mml:annotation encoding="application/x-tex">Q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> by making identifications on a face of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Q"> <mml:semantics> <mml:mi>Q</mml:mi> <mml:annotation encoding="application/x-tex">Q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Some applications of this result to measure preserving homeomorphisms on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are given: (1) The first is concerned with which measures on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are equivalent to each other by homeomorphisms. (2) The second application is about approximating invertible Borel measurable transformations of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> by measure preserving homeomorphisms of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. (3) The final application is concerned with generic properties of measure preserving homeomorphisms of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p> |
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spelling | Prasad, V. S. 0002-9939 1088-6826 American Mathematical Society (AMS) Applied Mathematics General Mathematics http://dx.doi.org/10.1090/s0002-9939-1983-0691301-0 <p>We show that every compact connected Hilbert cube manifold <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> can be obtained from the Hilbert cube <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Q"> <mml:semantics> <mml:mi>Q</mml:mi> <mml:annotation encoding="application/x-tex">Q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> by making identifications on a face of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Q"> <mml:semantics> <mml:mi>Q</mml:mi> <mml:annotation encoding="application/x-tex">Q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Some applications of this result to measure preserving homeomorphisms on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are given: (1) The first is concerned with which measures on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are equivalent to each other by homeomorphisms. (2) The second application is about approximating invertible Borel measurable transformations of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> by measure preserving homeomorphisms of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. (3) The final application is concerned with generic properties of measure preserving homeomorphisms of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p> A mapping theorem for Hilbert cube manifolds Proceedings of the American Mathematical Society |
spellingShingle | Prasad, V. S., Proceedings of the American Mathematical Society, A mapping theorem for Hilbert cube manifolds, Applied Mathematics, General Mathematics |
title | A mapping theorem for Hilbert cube manifolds |
title_full | A mapping theorem for Hilbert cube manifolds |
title_fullStr | A mapping theorem for Hilbert cube manifolds |
title_full_unstemmed | A mapping theorem for Hilbert cube manifolds |
title_short | A mapping theorem for Hilbert cube manifolds |
title_sort | a mapping theorem for hilbert cube manifolds |
title_unstemmed | A mapping theorem for Hilbert cube manifolds |
topic | Applied Mathematics, General Mathematics |
url | http://dx.doi.org/10.1090/s0002-9939-1983-0691301-0 |