If a vector field has only nondegenerate zeros then the number of zeros is bounded

"if a vector field has only nondegenerate zeros then the number of zeros is bounded"
With no idea how to show that without using Poincare-Hopf Theorem. Any proof possible without using any concept from algebraic topology?
 

lavinia

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Re: if a vector field has only nondegenerate zeros then the number of zeros is bounde

"if a vector field has only nondegenerate zeros then the number of zeros is bounded"
With no idea how to show that without using Poincare-Hopf Theorem. Any proof possible without using any concept from algebraic topology?
A non-degenerate zero is isolated - I think
 
489
0
Re: if a vector field has only nondegenerate zeros then the number of zeros is bounde

It's not true if the space isn't compact.
 

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