Bundle Maps Over A Common Base
Let πE:E→ M and πF:F→ M be fiber bundles over a space M. Then a bundle map from E to F over M is a continuous map φ:E→ F such that . That is, the diagram
should commute. Equivalently, for any point x in M, φ maps the fiber Ex = πE−1({x}) of E over x to the fiber Fx = πF−1({x}) of F over x.
Read more about this topic: Bundle Map
Famous quotes containing the words bundle, maps, common and/or base:
““There is Lowell, who’s striving Parnassus to climb
With a whole bale of isms tied together with rhyme,
He might get on alone, spite of brambles and boulders,
But he can’t with that bundle he has on his shoulders,
The top of the hill he will ne’er come nigh reaching
Till he learns the distinction ‘twixt singing and preaching;”
—James Russell Lowell (1819–1891)
“The faces of most American women over thirty are relief maps of petulant and bewildered unhappiness.”
—F. Scott Fitzgerald (1896–1940)
“Commercial jazz, soap opera, pulp fiction, comic strips, the movies set the images, mannerisms, standards, and aims of the urban masses. In one way or another, everyone is equal before these cultural machines; like technology itself, the mass media are nearly universal in their incidence and appeal. They are a kind of common denominator, a kind of scheme for pre-scheduled, mass emotions.”
—C. Wright Mills (1916–62)
“What if it tempt you toward the flood, my lord,
Or to the dreadful summit of the cliff
That beetles o’er his base into the sea,
And there assume some other horrible form
Which might deprive your sovereignty of reason,
And draw you into madness?”
—William Shakespeare (1564–1616)