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:
“We styled ourselves the Knights of the Umbrella and the Bundle; for, wherever we went ... the umbrella and the bundle went with us; for we wished to be ready to digress at any moment. We made it our home nowhere in particular, but everywhere where our umbrella and bundle were.”
—Henry David Thoreau (1817–1862)
“The faces of most American women over thirty are relief maps of petulant and bewildered unhappiness.”
—F. Scott Fitzgerald (1896–1940)
“There were none of the small deer up there; they are more common about the settlements. One ran into the city of Bangor two years before, and jumped through a window of costly plate glass, and then into a mirror, where it thought it recognized one of its kind.... This the inhabitants speak of as the deer that went a-shopping.”
—Henry David Thoreau (1817–1862)
“The highest perfection of politeness is only a beautiful edifice, built, from the base to the dome, of ungraceful and gilded forms of charitable and unselfish lying.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)