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:
“In the quilts I had found good objects—hospitable, warm, with soft edges yet resistant, with boundaries yet suggesting a continuous safe expanse, a field that could be bundled, a bundle that could be unfurled, portable equipment, light, washable, long-lasting, colorful, versatile, functional and ornamental, private and universal, mine and thine.”
—Radka Donnell-Vogt, U.S. quiltmaker. As quoted in Lives and Works, by Lynn F. Miller and Sally S. Swenson (1981)
“Living in cities is an art, and we need the vocabulary of art, of style, to describe the peculiar relationship between man and material that exists in the continual creative play of urban living. The city as we imagine it, then, soft city of illusion, myth, aspiration, and nightmare, is as real, maybe more real, than the hard city one can locate on maps in statistics, in monographs on urban sociology and demography and architecture.”
—Jonathan Raban (b. 1942)
“My hobby more and more is likely to be common school education, or universal education.”
—Rutherford Birchard Hayes (1822–1893)
“Shall we now
Contaminate our fingers with base bribes,
And sell the mighty space of our large honors
For so much trash as may be grasped thus?
I had rather be a dog and bay the moon
Than such a Roman.”
—William Shakespeare (1564–1616)