A characterization of manifold decompositions satisfying the disjoint triples property

Author:
Dennis J. Garity

Journal:
Proc. Amer. Math. Soc. **83** (1981), 833-838

MSC:
Primary 54B15; Secondary 57N15

MathSciNet review:
630031

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Abstract: A metric space satisfies the Disjoint Triples Property if maps , and from into are approximable by maps , and with . Those CE decompositions of manifolds satisfying 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 is secretly 0-dimensional where is a CE usc decomposition of , , with finite dimensional.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1981-0630031-6

Keywords:
Cell-like decomposition,
cellular set,
disjoint disks property,
disjoint triples property,
intrinsic dimension,
null sequence,
secret dimension,
shrinkable

Article copyright:
© Copyright 1981
American Mathematical Society