On the Connection of Degree Theory and 0-epi Maps1

We show that in a large class of continuous operators on Jordan domains the 0-epi maps are precisely those maps with nonzero degree. The class contains in particular perturbations of the identity by countably 1/2-condensing operators. This implies that the example of Z. Ding (1996, J. Math. Anal. Appl. 199, 458–468) contains a mistake.