For stabilities of differentiate mappings of differential manifolds, the following conjectures have been given in (1)The conjecture for r-stability. For any two paracompact differential manifolds V and M, almost every...For stabilities of differentiate mappings of differential manifolds, the following conjectures have been given in (1)The conjecture for r-stability. For any two paracompact differential manifolds V and M, almost every mapping in L(V, M, ∞) is r-stable. In the conjecture for r-stability, 'almost every' means 'except for a countable union of closed sets' without interior. When r = ∞, we call it the Strong Conjecture; and when r = 0, 1, we call it the Weak Conjecture and the Feeble Conjecture respectively. In [1] it was proved that when ∞≥ r≥ 2, the Conjecture for r-stability is false. Thus the Weak Conjecture and the展开更多
文摘For stabilities of differentiate mappings of differential manifolds, the following conjectures have been given in (1)The conjecture for r-stability. For any two paracompact differential manifolds V and M, almost every mapping in L(V, M, ∞) is r-stable. In the conjecture for r-stability, 'almost every' means 'except for a countable union of closed sets' without interior. When r = ∞, we call it the Strong Conjecture; and when r = 0, 1, we call it the Weak Conjecture and the Feeble Conjecture respectively. In [1] it was proved that when ∞≥ r≥ 2, the Conjecture for r-stability is false. Thus the Weak Conjecture and the
