| 翻訳と辞書 |
bundle map
In mathematics, a bundle map (or bundle morphism) is a morphism in the category of fiber bundles. There are two distinct, but closely related, notions of bundle map, depending on whether the fiber bundles in question have a common base space. There are also several variations on the basic theme, depending on precisely which category of fiber bundles is under consideration. In the first three sections, we will consider general fiber bundles in the category of topological spaces. Then in the fourth section, some other examples will be given.
==Bundle maps over a common base==
Let ''π''''E'':''E''→ ''M'' and ''π''''F'':''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 ''E''''x'' = ''π''''E''−1() of ''E'' over ''x'' to the fiber ''F''''x'' = ''π''''F''−1() of ''F'' over ''x''.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「bundle map」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|