Math Homework Problem

Muirhead

United States556 Posts

March 08 2008 06:57 GMT

I'm probably just being stupid, but for some reason this seems difficult to me. I'm posting it in a few places on the internet in case someone can help me out. Thanks in advance!

Let M be a connected, compact, smooth manifold without boundary. Let V denote the (real) vector space of all smooth functions from M into the real line. Call a subspace H of V invariant if whenever h is in H and g is a diffeomorphism of M then h composed with g is in H. Prove that the only invariant subspaces are {0}, V, and the set of constant functions on M.

evanthebouncy!

United States12796 Posts

March 08 2008 08:35 GMT

Lol this is beyond me, maybe next year xD

and to ur quote:
Algebraic Geometry or Starcraft?

Algebraic Geometry any day.

Spenguin

Australia3316 Posts

March 08 2008 12:25 GMT

It makes my problem seem Butt Secks Man like.

Muirhead

United States556 Posts

March 08 2008 21:49 GMT

This is due on Monday if anyone can help by then. Nobody on AoPS can solve it quickly so I feel it must be difficult.

JacobDaKung

Sweden132 Posts

March 08 2008 22:42 GMT

well, I cant rember the specifics but, first u have to show that it is one-to-one mapping. Meaning u need all dimensions to plot the whole R-axis then. Then u show that the only spaces that maps one-to-one on those requierments are {0} and V.
The specifics Im not sure about, but I think this is the way to go.
/Jacob

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