A First Course in Topology : Continuity and Dimension

How many dimensions does our universe require for a comprehensivephysical description? In 1905, Poincare argued philosophically about thenecessity of the three familiar dimensions, while recent research isbased on 11 dimensions or even 23 dimensions. The notion of dimensionitself presented a basic problem to the pioneers of topology. Cantorasked if dimension was a topological feature of Euclidean space. Toanswer this question, some important topological ideas were introducedby Brouwer, giving shape to a subject whose development dominated thetwentieth century.