Continuous Vector Bundle
A continuous vector bundle is a vector bundle pi:E->M with only the structure of a topological manifold. The map pi is continuous. It has no smooth structure or bundle metric.
See also
Bundle, Manifold, Vector BundleThis entry contributed by Todd Rowland
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Rowland, Todd. "Continuous Vector Bundle." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ContinuousVectorBundle.html