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From Wikipedia, the free encyclopedia
In mathematics, a Banach bundle is a fiber bundle over a topological Hausdorff space, such that each fiber has the structure of a Banach space.
Let be a topological Hausdorff space, a (continuous) Banach bundle over is a tuple , where is a topological Hausdorff space, and is a continuous, open surjection, such that each fiber is a Banach space. Which satisfies the following conditions:
If the map is only upper semi-continuous, is called upper semi-continuous bundle.
Let A be a Banach space, X be a topological Hausdorff space. Define and by . Then is a Banach bundle, called the trivial bundle
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