• Jeremy GrayEmail author
Part of the Springer Undergraduate Mathematics Series book series (SUMS)


Here we look briefly at problems to do with curves and surfaces, lengths and areas, starting with the great question of: what is a continuous curve? In particular, does a simple closed curve on a sphere have a simply-connected interior and a simply-connected exterior? Then we return to the problem of distinguishing a the unit interval from the unit square, and we conclude by showing how curves can have areas (non-zero Lebesgue measure). In this way we shall pick up some of the roots of both point-set and algebraic or geometric topology.


Simple Polygon Simple Closed Curve Geometric Topology Koch Curve Straight Side 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsThe Open UniversityMilton KeynesUK
  2. 2.University of WarwickCoventryUK

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