Titlebook: Spaces of Continuous Functions; G.L.M. Groenewegen,A.C.M. van Rooij Book 2016 Atlantis Press and the author(s) 2016 Spaces of Continuous F

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,Yosida’s Representation Theorem,Our main result, as mentioned in the preamble to Chap. ., is Yosida’s Theorem, characterizing the Riesz spaces that are isomorphic to .(.) for some compact Hausdorff space .. At the background we have Alaoglu’s Theorem, giving us the space . we need.

Ceramic

,The Stone-Čech Compactification,When dealing with a metric space it is often useful to form its completion. Similarly, it may be useful to embed a topological space . in a compact Hausdorff space, preferably as a dense subset.

Paradox

Evaluations,Let . be a topological space.

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思想

The Riesz Representation Theorem,The integral of a continuous function on . may be viewed as the average value of that function. Sometimes it is desirable to have at one’s disposal a method of averaging functions on . that gives different weights to different parts of the interval.

ineluctable

Banach Algebras,For compact ., .(.) is an ordered vector space. Yosida’s Theorem characterizes those ordered vector spaces that are “isomorphic” with a .(.). In this chapter we obtain an analogous result for a multiplication instead of an ordering.

顾客

Multiple

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