Number of Nondegenerate Zeros of Vector Field Bounded

[huyichen]

"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]

"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

 

[zhentil]

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