Space-Filling Curves (Universitext) - Tapa blanda

The subject of space-filling curves has generated a great deal of interest in the 100 years since the first such curve was discovered by Peano. Cantor, Hilbert, Moore, Knopp, Lebesgue and Polya are among the prominent mathematicians who have contributed to the field. However, there have been no comprehensive treatment of the subject since Siepinsky's in 1912. Cantor showed in 1878 that the number of points on an interval is the same as the number of points in a square, while in 1890 Peano showed that there is indeed a continuous curve that maps all points of a line onto all points of a square, although the curve exists only as a limit of very convoluted curves. This book discusses generalizations of Peano's solution and the properties that such curves must possess. It also discusses fractals in this context.