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Erschienen in:
2015 | OriginalPaper | Buchkapitel
7. Approach Theory Meets Topology
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Abstract
In Chaps. 7–11 we study applications of approach theory to various areas of mathematics. Here we highlight two areas in topology, namely function spaces and the Cech-Stone compactification. In the first section we treat function spaces, starting from arbitrary approach spaces and uniform gauge spaces. The results are applicable to any situation where for instance a choice has been made of a particular metric for a topology or a uniformity. In the second section we study the approach version of the Cech-Stone compactification of an Atsuji space, and in particular of the natural numbers, in more detail.