Change of variables for integration. The integral formulation of the degree gives the same as the weighted sum formula. If p 1 and p 2 are 'close', then degree is constant.
Degrees are equal for f and g close together.
If f and g are homotopic, then the degrees are equal. Weierstrass approximation theorem. Degree is defined for continuous functions by taking a close C 1 approximation. These results now hold for version 4 of the definition. If f and g are close, then degree is constant.