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| Simmons G.F. — Introduction to topology and modern analysis |
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| Предметный указатель |
Quotient, space 193—194
Radical 314
Real line 21
Real line, absolute value on 52
Real line, extended 56
Real line, least upper bound property 21 45
Real line, usual metric on 52
Rectangle, closed 101 119
Rectangle, open 101 119
Reflexivity, of normed linear space 232
Reflexivity, of relation 27 43
Relation (binary) 26
Relation antisymmetric 43
Relation circular 31
Relation equivalence 27
Relation partial order 7 43
Relation reflexive 27 43
Relation symmetric 27
Relation transitive 27 43
Relation triangular 31
Relative topology 93
Representation, of algebra 210
Representation, of B*-algebra 325 326
Representation, of Banach algebra 305
Representation, of Banach space 234
Representation, of Boolean algebra 353
Representation, of Boolean ring 351
Representation, of commutative C*-algebra 332—334
Representation, of commutative semi-simple Banach algebra 322
Representation, of group 181
Representation, of Hilbert space 260
Representation, of linear space 201—202
Representation, of ring 188 190
Resolvent equation 309
Resolvent of an element 309
Resolvent set 309
Rickart, C.E. ix 326n
Riemann sphere 163
Riemann, B. 49
Riesz representation theorem 226
Riesz — Fischer theorem 257—258
Riesz, F. 49 226 296n
Ring, commutative 183
Ring, coset in 18
Ring, division 184
Ring, divisor of zero 183
Ring, elements in, invertible 183
Ring, elements in, non-singular 183
Ring, elements in, regular 183
Ring, elements in, singular 183
Ring, homomorphism 188
Ring, ideal in 184
Ring, inverses 183
Ring, isomorphism 188
Ring, kernel 188
Ring, of integers mod m 182
Ring, of operators 303
Ring, of sets 14 182
Ring, quotient 187
Ring, subring of 184
Ring, with identity 183
Robbins, H. 94 338
Russell's paradox 6
Russell, B. 7
Scalars 80 191 214
Schauder's fixed point theorem 338
Schroeder — Bernstein theorem 29
Schwartz's inequality 246
Schwartz, J.T. ix 220 232n
Second conjugate space 231
Second countable space 99-100
Self-adjoint operator 266
Self-adjoint subalgebra of  303
Semi-simple algebra 316
Separable space 96
Sequence, Cauchy 71
Sequence, convergent 50 70 132
Sequence, limit of 50 71 132
Sequentially compact metric space 121
Set (s), universal 5 7—8
Set Mappings 18—19
Set(s) 4
Set(s) abnormal 6
Set(s) Boolean algebra 12 344
Set(s) boundary 68 97
Set(s) boundary point 68 97
Set(s) bounded 58
Set(s) Cantor 67
Set(s) Cartesian product 21
Set(s) closed 65 95
Set(s), closure 68 96
Set(s), complement 10
Set(s), contrasted with space 5
Set(s), convex 148
Set(s), countable 34
Set(s), countably infinite 34
Set(s), dense (everywhere dense) 70 96
Set(s), derived 90
Set(s), diagrams 8
Set(s), diameter 5
Set(s), difference of 13
Set(s), disjoint 9
Set(s), distance from point to 58
Set(s), empty 5
Set(s), equality 5
Set(s), equivalence 27
Set(s), finite 5
Set(s), finite intersection 12
Set(s), finite union 12
Set(s), inclusion 6
Set(s), index 11
Set(s), infinite 5
Set(s), interior of 63 07
Set(s), interior point 53 97
Set(s), intersection 9 11
Set(s), linearly ordered 44
Set(s), neighborhood of 96
Set(s), normal 6
Set(s), nowhere dense 74 99
Set(s), numerical equivalence 28 32
Set(s), of first category 75n
Set(s), of second category 75
Set(s), open 60 91 92
Set(s), open basic 99
Set(s), open subbasic 101
Set(s), open-closed 349
Set(s), orthonormal 251
Set(s), orthonormal complete 255
Set(s), partially ordered 4 44
Set(s), partition 26
Set(s), perfect 99
Set(s), product 23—25
Set(s), proper subset 6
Set(s), proper superset 6
Set(s), ring 14
Set(s), subset 5
Set(s), superset 5
Set(s), symmetric difference 13
| Set(s), totally ordered 44
Set(s), uncountable 36
Set(s), union 8 11
Sierpinski, W. 42n 46n
Similarity for matrices 286
Smirnov, Y.M. 139
Space, contrasted with set see also “Banach space; Hilbert space; Linear space; Metric space; Normed linear space” 5n
Space, Euclidean 24 87 90 214
Space, fixed point 337—338
Space, metrizable 93
Space, of maximal ideals 319
Space, unitary 24 90 214
Space-filling curve(s) 341
Space-filling curve(s) Hilbert's 341—342
Spectral radius 310
Spectral radius formula 312
Spectral resolution 280
Spectral theorem 280 290
Spectral theorem, generalized forms 295—297 334
Spectrum, of element in Banach algebra 308
Spectrum, of operator 289 29
Sphere, closed 66
Sphere, closed unit 217 232
Sphere, open 59
Stone representation theorem, for Boolean algebras 333
Stone representation theorem, for Boolean rings 351
Stone — Cech compactification 141 331
Stone — Weierstrass theorem(s), complex 161
Stone — Weierstrass theorem(s), extended 166—167
Stone — Weierstrass theorem(s), real 160
Stone, M.H. see also “Banach-Stone theorem” 141n 153 161n
STRIPS 101
Strong topology 232
Strongest topology 104
Subbasc, closed 112
Subbasc, open 101
Subcover 111
Supremum 45
Symmetry 27 51
Sz.-Nagy, B. 226 296n
Taylor, A.E. 215n 239n 248
Tietze extension theorem 136
Topological divisor of zero 307
Topological space(s) 91 92
Topological space(s)  130
Topological space(s) compact 110 111
Topological space(s) compact subspace 111
Topological space(s) completely regular 133
Topological space(s) components 146
Topological space(s) connected 142 143
Topological space(s) connected subspace 143
Topological space(s) countably 114
Topological space(s) disconnected 143
Topological space(s) disconnection 143
Topological space(s) discrete 93
Topological space(s) discrete two-point 144
Topological space(s) first countable 100n
Topological space(s) Hausdorff 130
Topological space(s) homeomorphic 94
Topological space(s) locally 120 162
Topological space(s) locally connected 151
Topological space(s) metrizable 93
Topological space(s) normal 133
Topological space(s) open base 99
Topological space(s) open subbase 101
Topological space(s) Peano 342n
Topological space(s) product 117
Topological space(s) second countable 99—100
Topological space(s) separable 96
Topological space(s) subspace 93
Topological space(s) totally disconnected 149
topology 92
Topology as branch of mathematics 94
Topology discrete 93
Topology generated by given class of sets 102
Topology open base 99
Topology open subbase 101
Topology product 116—117
Topology relative 93
Topology strong, on normed linear space 232
Topology strongest 104
Topology usual 92
Topology weak operator 303
Topology weak*, on conjugate space 232—233
Topology weak, generated by set of mappings 105
Topology weak, generated by set of mappings on normed linear space 232
Topology weakest 104
Total matrix algebra 284
Totally bounded metric space 123
Totally disconnected space 149
Totally ordered set 44
Transitivity 27 43
Triangle inequality 51
Tychonoff's theorem 119
Uniform boundedness theorem 211 239—240
Uniform continuity 77
Uniform convergence 83
Uniform norm 216
Uniformly bounded functions 128n
Uniformly convex Banach space 248
Unit circle 5
Unit disc, closed 5
Unit disc, open 5
Unitary operator 272
Unitary space, infinite-dimensional 90
Unitary space, n-dlmensional 24 90 214
Universal set 5 7—8
Upper bound, least 45
Urysohn's imbedding theorem 138
Urysohn's lemma 135
Usual topology on metric space 92
Vector space sec “Linear space”
Vectors 81 86—87 191
Vectors characteristic 278n
Vectors eigen- 278
Vectors linearly dependent 196—197
Vectors linearly independent 196-197
Vectors orthogonal 249
Vectors, proper 278n
von Neumann algebra 303
W*-algebra 303
Wallman, H. 150
Weak operator topology 303
Weak topology, generated by set of mappings 105
Weak topology, on normed linear space 232
Weak* topology on conjugate space 232—233
Weakest topology 104
Weierstrass approximation theorem 154 161
Weierstrass Intermediate Value Theorem 142 144
Weierstrass, K. see also “Bolzano — Weierstrasg; Stone — Weierstrass” 49
Wilder, R.L. 6 39n 46n 343
Zaanen, A.C. 215n
Zero 54 80 179
Zero divisor 183
Zero divisor topological 307
Zero space 192
Zorn's lemma 45—46
Zygmund, A. 240
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