Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54B15, 57N15

Retrieve articles in all journals with MSC: 54B15, 57N15

Additional Information

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