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 the, relation between, relation and/or notions:
“We shall never resolve the enigma of the relation between the negative foundations of greatness and that greatness itself.”
—Jean Baudrillard (b. 1929)
“You know there are no secrets in America. It’s quite different in England, where people think of a secret as a shared relation between two people.”
—W.H. (Wystan Hugh)
“Among the most valuable but least appreciated experiences parenthood can provide are the opportunities it offers for exploring, reliving, and resolving one’s own childhood problems in the context of one’s relation to one’s child.”
—Bruno Bettelheim (20th century)
“Shelley is truth itself—and honour itself—notwithstanding his out-of-the-way notions about religion.”
—George Gordon Noel Byron (1788–1824)