INDEX 415

Tietze extension theorem, 130total variation, 198totally ordered, 50trapezoid rule, 228triangle inequality, 33, 370trichotomy, 14trigonometric functions, 169

uncountableunit interval, 78

uniform convergence, 297sequence, 121, 156series, 123

uniformly bounded, 126uniformly Cauchy, 122

sequence, 122uniformly continuous, 118unit interval

uncountable, 78upper semicontinuous, 119

variation of constants formula, 312Vitali covering, 358Vitali covering theorem, 356

vitali covers, 358

Wallis formula, 218Weierstrass, 106Weierstrass approximation

estimate, 124Weierstrass approximation theorem, 125Weierstrass Bolzano theorem, 188Weierstrass M test, 123, 302well ordered, 19winding number, 286

Young’s integral, 378estimates, 378

Zermelo, 53