【摘要】 光滑映射芽各种稳定性的讨论，一直是奇点理论的一个重要部分． Ｔｈｏｍ Ｒ．［１］在创立突变论时，提出了映射芽的，ｒ－开折的稳定性理论．Ｗａｓｓｅｒｍａｎｎ Ｇ．［２］将之发展为开折的（ｒ，ｓ）稳定理论．本文将他们的结论发展为（ｒ１，ｒ２，…，ｒｄ）稳定性，在任意的分级情况下，得到强稳定性、弱稳定性及无穷小稳定性的等价性，并得到了一些基本结果．更多还原

【Abstract】 The discussion of various stabilities of smooth map-germs is an important part of singularity theory. While Thorn R. [1] established catastrophe theory, he gave a theory of stability of r-unfoldings of map germs. Wassermann G.[2] developed a theory of (r, s)-stability of unfoldings. In this paper we generalize them to (r1 ,... ,rd)-stability. For any Integer d, we prove equivalence of strong-, weak- and infinitesimal stabilities among other basic results.更多还原