Flowbox manifolds

Authors:
J. M. Aarts and L. G. Oversteegen

Journal:
Trans. Amer. Math. Soc. **327** (1991), 449-463

MSC:
Primary 54H20; Secondary 54E99

MathSciNet review:
1042286

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Abstract: A separable and metrizable space is called a flowbox manifold if there exists a base for the open sets each of whose elements has a product structure with the reals as a factor such that a natural consistency condition is met. We show how flowbox manifolds can be divided into orientable and nonorientable ones. We prove that a space is an orientable flowbox manifold if and only if can be endowed with the structure of a flow without restpoints. In this way we generalize Whitney's theory of regular families of curves so as to include self-entwined curves in general separable metric spaces. All spaces under consideration are separable and metrizable.

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DOI:
https://doi.org/10.1090/S0002-9947-1991-1042286-8

Article copyright:
© Copyright 1991
American Mathematical Society