Topological and Ordered Groups

E. S. Lyapin, A. Ya. Aizenshtat and M. M. Lesokhin

Chapter Chapter 8 in Exercises in Group Theory, 1972, pp 161-184 from Springer

Abstract: Abstract Let M be a set and let ρ be a mapping of the Cartesian product M × M into the set of nonnegative real numbers [in other words, to every pair (x, y) of elements in M associate a real number ρ(x, y) ⩾ 0]. This mapping is called a metric, or a distance function (d is often used instead of ρ) if it satisfies the following three conditions: 1) ρ(x, y) = 0 if and only if x = y; 2) ρ(x, y) = ρ(y, x) for all x, y ∈ M; 3) ρ(x, y) ⩾ ρ(x, z) + ρ(z, y) for all x, y, z ∈ M.

Date: 1972
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DOI: 10.1007/978-1-4613-4589-3_8

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