DOI: 10.36347/sjet

Pages: 263-266

In the first part of this paper, it firstly takes x  x0 and x as an example. It presents that the unary function has Heine theorem of the normal limit existence and promotion form, and also Heine theorem of the abnormal limit existence. Secondly, it presents that Heine theorem of normal unilateral limit existence has conditions with stronger forms. Finally, it shows that the multivariate function has Heine theorem of normal and abnormal limit existence. In the second part, it lists some application of Heine theorem.