Homeomorphism between R and {0}xR

[math6]

Hi friends !

Let E be a holomorphic vector bundle over a complex manifold M . We identify M with the zero section of E .
i would like to know waht's mean "" We identify M with the zero section of E ".
thnx :)

 

[lavinia]

Hi friends !

Let E be a holomorphic vector bundle over a complex manifold M . We identify M with the zero section of E .
i would like to know waht's mean "" We identify M with the zero section of E ".
thnx :)

For any vector bundle, the set of zero vectors across the manifold is diffeomorphic to the manifold. The map x->(x.0) maps the manifold to the zero section. It is easy to check that it is an embedding.

 

[mathwonk]

can you show that the real numbers R are homeomorphic to the subset {0}xR of RxR?