Given tex2html_wrap81 with a fibre F and given f:N- tex2html_wrap82 M, define a bundle whose base space is N and fibre F s.t. tex2html_wrap83 . Can define transition functions by tex2html_wrap84 .

Theorem: if f ang g are homotopic maps from N to M than tex2html_wrap85 and tex2html_wrap86 are equivalent bundles.

Corollary: if M is contractible to a point, than any bundle over M is trivial




source
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