Titlebook: Mathematical Methods for Economic Theory 2; James C. Moore Textbook 1999 Springer-Verlag Berlin Heidelberg 1999 Connected space.Economic T

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Additional Topics in Topology,sets, metrics, and weak orders. In this section, we will study methods of generating new topologies from other topologies. We begin by investigating subspace, or relative, topologies. The basic idea here is exactly that which we used in defining relatively open sets in Chapter 1.

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Correspondences,urns out, all of the continuity definitions with which I am familiar have found their way into economic theory, and such notions are of central importance in many theoretical developments in economics. We define a correspondence as follows.

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Banach Spaces,intended to present can be done as easily for Banach spaces as for the special case of a Hilbert space. Consequently, in most of this chapter we will actually be dealing with Banach spaces; hence the title.

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Selection and Fixed-Point Theorems,h we will be studying in this chapter consists of some of the most useful mathematical topics which I know about. We begin this study by presenting what is, essentially, Berge’s development of his maximum thoerem (12.2, 12.3, and 12.4, below). We will then discuss a result which generalizes Berge’s

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Textbook 1999equently useful in economics, but for which exact statements and proofs are rather difficult to find; for example, a number of results on convex sets and their separation by hyperplanes, some results on correspondences, and some results concerning support functions and their duals. Secondly, while t

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