Abstract
We assume a basic knowledge of general topology and integration theory (as found, for example, in [91], [104], [130], and [253]). The purpose of this chapter is to present some special results which are not necessarily found in general references. In section 4 we prove an interpolation theorem and investigate when compact Hausdorff spaces can be mapped continously onto the closed unit interval [0, 1]. A brief development of dispersed spaces and their relationship to spaces of ordinal numbers is given in section 5. Section 6 is devoted to a study of the Cantor set and section 7 is concerned with extremally disconnected compact Hausdorff spaces and their role as projectives (in the category of compact Hausdorff spaces and continuous maps). In section eight we briefly develop the theory of regular Borel measures and prove representation theorems for C(T,ℝ)* (and C(T,ℂ)*).
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© 1974 Springer-Verlag Berlin · Heidelberg
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Lacey, H.E. (1974). Some Aspects of Topology and Regular Borel Measures. In: The Isometric Theory of Classical Banach Spaces. Die Grundlehren der mathematischen Wissenschaften, vol 208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65762-7_2
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DOI: https://doi.org/10.1007/978-3-642-65762-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65764-1
Online ISBN: 978-3-642-65762-7
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