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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A characterization of manifold decompositions satisfying the disjoint triples property
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by Dennis J. Garity PDF
Proc. Amer. Math. Soc. 83 (1981), 833-838 Request permission

Abstract:

A metric space $X$ satisfies the Disjoint Triples Property $({\text {D}}{{\text {D}}_{\text {3}}})$ if maps ${f_1}$, ${f_2}$ and ${f_3}$ from ${B^2}$ into $X$ are approximable by maps ${\tilde f_1}$, ${\tilde f_2}$ and ${\tilde f_3}$ with $\cap _{i = 1}^3{\tilde f_i}({B^2}) = \emptyset$. Those CE decompositions of manifolds satisfying ${\text {D}}{{\text {D}}_3}$ and yielding finite-dimensional nonmanifold decomposition spaces are shown to be precisely those intrinsically $0$-dimensional decompositions which yield nonshrinkable null cellular decompositions under amalgamation. This characterization results in another proof of the fact that ${E^n}/G \times {E^1}$ is secretly $0$-dimensional where $G$ is a CE usc decomposition of ${E^n}$, $n \geqslant 4$, with ${E^n}/G$ finite dimensional.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 83 (1981), 833-838
  • MSC: Primary 54B15; Secondary 57N15
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0630031-6
  • MathSciNet review: 630031