Notes on Topological Stability
Notes on Topological Stability
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拓扑稳定性注意事项
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发表时间：
2012
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通讯作者：
J. Mather
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作者：
J. Mather
这些笔记是作者在1970年春天所作的一系列讲座的第一章的一部分。本文的最终目的是证明对任意有限维流形N和P（其中N是紧的），拓扑稳定映射集构成C∞（N，P）的稠密子集的定理。第一章研究了E-Whitney的分层集和分层映射理论。连接的材料在这些笔记与定理的密度拓扑稳定的映射出现在第11节，在那里我们给汤姆的第二个合痕引理。这个结果给出了两个映射拓扑等价的充分条件。
These notes are part of the first chapter of a series of lectures given by the author in the spring of 1970. The ultimate aim of these notes will be to prove the theorem that the set of topologically stable mappings form a dense subset of C∞(N,P ) for any finite dimensional manifolds N and P where N is compact. The first chapter is a study of Thom–Whitney theory of stratified sets and stratified mappings. The connection of the material in these notes with the theorem on the density of topologically stable mappings appears in Section 11, where we give Thom’s second isotopy lemma. This result gives sufficient conditions for two mappings to be topologically equivalent.