Flowbox manifolds

Aarts, J. M.; Oversteegen, L. G.

doi:10.1090/S0002-9947-1991-1042286-8

Flowbox manifolds
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by J. M. Aarts and L. G. Oversteegen

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

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

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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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