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2005 | OriginalPaper | Buchkapitel
Introduction
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Topology is one of the better-known areas of modern mathematics. Most people have heard the statement that a topologist is someone who cannot tell the difference between a tea cup and a doughnut. This is true, and we will see why in Chapter 5. Clearly, then, topology ignores some things and perceives similarities between apparently dissimilar objects. As we will discover, the key to what topology ignores, and to what it concentrates on, is the behaviour of continuous functions. Topology studies the ways in which the properties of the domain and range determine the behaviour of a continuous function.