## 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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### References:

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