集值映射的連續性概念首先是由G. Bouligand 與K. Kuratowski 所提出。而集值映射的微分性有兩種方式定義。一種是延續古典微分的方式定義；另一種是法錐的方式定義，是由B.S. Mordukhovich 所提出。在本篇論文中，我們研究探討集值映射的各種連續性之定義與微分性之定義。

The concepts of continuity for set-valued mappings were introduced by G. Bouligand and K. Kuratowski. There are two ways defining differentiability of set-valued mapping. One is defined by classical differentiability theorem and another is defined by normal cone which was introduced by B.S. Mordukhovich. In this thesis, we survey various definitions of continuity and differentiability for set-valued mapping.

1 Introduction ..................................................1
2 Preliminaries ...............................................3
3 Continuity of Set-Valued maps................. 4
4 Generalized Differentiation .......................11
4.1 Primal Space Approach......................... 11
4.2 Dual Space Approach ............................16

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