MATH 328: Chapter 4: Theorem of Arzela-Ascoli
نویسنده
چکیده
In this chapter, we begin to discuss the ways in which R differs from C[0,1]. In particular, we compare the characterization of compact subsets of R by HeineBorel with the characterization of compact subsets of C[0,1] by Arzela-Ascoli. We find that subsets of C[0,1] must satisfy more conditions than subsets of R if they are to be compact. Before we can begin to investigate this, we have a few preliminary definitions to recall from point-set topology. In the following definitions, X is our normed vector space, A is a subset of the vector space.
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تاریخ انتشار 2005