About the Book
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 45. Chapters: Topological space, Euclidean space, Cantor set, Sierpinski triangle, Sierpinski carpet, Real line, Finite topological space, Real projective line, Sierpi ski space, Hyperbolic space, Homology sphere, Long line, Particular point topology, Menger sponge, Ultrametric space, Box topology, Trivial topology, Extension topology, Hawaiian earring, Cantor space, Rose, Moore plane, Hilbert cube, Smith-Volterra-Cantor set, Comb space, Lower limit topology, Appert topology, K-topology, Sorgenfrey plane, Topologist's sine curve, Hjalmar Ekdal topology, Pseudomanifold, Evenly spaced integer topology, First uncountable ordinal, Hedgehog space, Partition topology, Lexicographic order topology on the unit square, Pseudocircle, Geometric topology, Infinite broom, Dogbone space, Half-disk topology, Dunce hat, Overlapping interval topology, Excluded point topology, Fort space, Interlocking interval topology, Prufer manifold, Tychonoff plank, Knaster-Kuratowski fan, Arens-Fort space, Countably compact space, Homotopy sphere, List of examples in general topology, Erd s space, Discrete two-point space. Excerpt: In mathematics, the Cantor set, introduced by German mathematician Georg Cantor in 1883 (but discovered in 1875 by Henry John Stephen Smith), is a set of points lying on a single line segment that has a number of remarkable and deep properties. Through consideration of it, Cantor and others helped lay the foundations of modern general topology. Although Cantor himself defined the set in a general, abstract way, the most common modern construction is the Cantor ternary set, built by removing the middle thirds of a line segment. Cantor himself only mentioned the ternary construction in passing, as an example of a more general idea, that of a perfect set that is nowhere dense. The Cantor ternary set is created by repeatedly deleting t...
