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Flowbox manifolds. (English) Zbl 0768.54027

Summary: 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 \(\mathfrak R\) as a factor such that a natural consistency condition is met. We show how flowbox manifolds can be divided into orientable and non-orientable 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.

MSC:

54H20 Topological dynamics (MSC2010)
54E99 Topological spaces with richer structures
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