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 between, relation and/or notions:
“There is a certain standard of grace and beauty which consists in a certain relation between our nature, such as it is, weak or strong, and the thing which pleases us. Whatever is formed according to this standard pleases us, be it house, song, discourse, verse, prose, woman, birds, rivers, trees, room, dress, and so on. Whatever is not made according to this standard displeases those who have good taste.”
—Blaise Pascal (1623–1662)
“Hesitation increases in relation to risk in equal proportion to age.”
—Ernest Hemingway (1899–1961)
“the full analysis of the notions of saying something and understanding what one said inevitably involves a concept which, as I will show in detail, essentially corresponds to the Cartesian idea of thought.”
—Zeno Vendler (b. 1921)