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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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 $ X$ 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 $ \operatorname{Re} $ 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 $ X$ is an orientable flowbox manifold if and only if $ X$ 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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