Introduction In the first place, what are the properties of space properly so called? ... 1st, it is continuous 2nd, it is infinite 3rd, it is of three dimensions .. . HENRI POINCARE, 19 So will the final theory be in 10, 11 or 12 dimen- sions? MICHIO KAKU, 19 As a separate branch of mathematics, topology is relatively you It was isolated as a collection of methods and problems by HEN POINCARE (1854-1912) in his pioneering paper Analysis situs of 18 The subsequent development of the subject was dramatic and top ogy was deeply influential in shaping the mathematics of the twenti century and today. So what is topology? In the popular understanding, objects l the Mobius band, the Klein bottle, and knots and links are the first be mentioned (or maybe the second after the misunderstanding abo topography is cleared up). Some folks can cite the joke that topo gists are mathematicians who cannot tell their donut from their cof cups. When I taught my first undergraduate courses in topology found I spent too much time developing a hierarchy of definitions a
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