Relation Between The Two Notions
It follows immediately from the definitions that a bundle map over M (in the first sense) is the same thing as a bundle map covering the identity map of M.
Conversely, general bundle maps can be reduced to bundle maps over a fixed base space using the notion of a pullback bundle. If πF:F→ N is a fiber bundle over N and f:M→ N is a continuous map, then the pullback of F by f is a fiber bundle f*F over M whose fiber over x is given by (f*F)x.= Ff(x). It then follows that a bundle map from E to F covering f is the same thing as a bundle map from E to f*F over M.
Read more about this topic: Bundle Map
Famous quotes containing the words relation and/or notions:
“You must realize that I was suffering from love and I knew him as intimately as I knew my own image in a mirror. In other words, I knew him only in relation to myself.”
—Angela Carter (1940–1992)
“Hang ideas! They are tramps, vagabonds, knocking at the back- door of your mind, each taking a little of your substance, each carrying away some crumb of that belief in a few simple notions you must cling to if you want to live decently and would like to die easy!”
—Joseph Conrad (1857–1924)