A continuous vector bundle is a vector bundle 
whose local trivializations and transition functions
are continuous. No smooth structure is assumed.
A continuous bundle metric can nevertheless be chosen under standard hypotheses,
such as when 
is paracompact.
Continuous Vector Bundle
See also
Bundle, Manifold, Vector BundlePortions of this entry contributed by Todd Rowland
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Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Continuous Vector Bundle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ContinuousVectorBundle.html