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