It is useful to have notions of a mapping between two fiber bundles.

The same is not true for other fiber bundles.

In fact, as their name suggests, they are fiber bundles.

There was no catwalk; they had to stand directly on the bottom fiber bundle.

Thus every microbundle can be refined to an actual fiber bundle in an essentially unique way.

First, one can consider fiber bundles in a different category of spaces.

That is, it actually constructs a fiber bundle with the given properties.

Development then focused on fiber bundles for image transmission.

These can be used in understanding and proving the product property for the Euler characteristic of a fiber bundle.

In general, fiber bundles over the circle are a special case of mapping tori.