Index 391

in a metric space, 172

Cauchy’s Mean Value Theorem, 94

Cauchy-Schwarz inequality, 165

cell

2-cell, 341

2-cell in

Rd,

354

3-cell, 360

3-cell in

Rd,

364

simple, 341

chain

0-chain, 366

1-chain, 366

p-chain, 369

in an ordered set, 383

Chain Rule, 86

in several variables, 237

change of coordinates, 266

polar, 264, 329

spherical, 265

change of parameter, 323, 343

change of variables, 241, 328

change of variables formula, 311, 313,

340, 358

characteristic function

of a set, 281

closed

ball, 174

curve, 194

relatively, 184

set, 174

closed differential form, 335, 373

closure, 176

coeﬃcients

of a power series, 148, 154

commutative group, 366

commutative law

for vector addition, 162

of addition, 16

of multiplication, 16

commutative ring, 16

of integers, 17

compact, 179

image, 198

metric space, 182

comparison test, 132

complement of a set, 4

complete

metric space, 172

ordered field, 23

completeness axiom, 23

component

connected, 186

function, 192

of a vector, 162, 164

composition

of continuous functions, 63, 193

of functions, 5

conditional convergence, 140

conditionally convergent series

rearrangement, 141

conical coordinates, 358

connected

image, 199

set, 184

subset of R, 185

connected component, 186

continuity

at a point, 60, 62, 193

of a power series sum, 150

of composite function, 63, 193

of vector functions, 191

uniform, 200

continuous function, 61

boundedness, 65

extension, 71

image, 67

max/min, 65

when uniformly continuous, 70

contraction mapping, 93

converge

pointwise, 203

uniformly, 203

convergence

absolute, 132

componentwise, 171

in

Rd,

177

in a metric space, 169

of a geometric series, 131

of sequences in R, 36

of sequences in Rd, 169

of series, 129

of series with non-negative terms, 132

pointwise, 74

uniform, 74

convex set, 253

countability

of the rational numbers, 378

countable set, 378

countably infinite, 378

Cramer’s Rule, 213

critical points, 89

crossing point, 245