 -set 127
 - set 127
 - dimensional chain 247
- dimensional cube 43
- dimensional space 43 227
 - space 119
 - space 129
Abelian group 244
Abscissa 50
Abscissaaxis 50
Absolute retract 150
Accessible point 271
Accumulation point 119
Additive family of sets 52
Aleph 93
Alexandrov theorem 167
Antinomy 74
Antipodes (theorem on) 274
Antoine arc 257
ARC 216
Arcwise connected space 217
Argument of a function 47
Axiom of Choice 45
Axioms of a topological space 118
Axioms of the theory of groups 244
Axioms of the theory of sets 32 44
Axis of abscissas 50
Axis of ordinates 50
Baire space 151
Baire theorem 165
Banach theorem 183 192
Barycentric coordinates 232
Base of a space 130 154
Betti group 251
Betti number 251
Bicompact space 190
Boolean algebra 33
Borel family of sets 55
Borel set 127
Borel theorem 171
Borel — Lebesgue theorem 172
Borsuk theorem 273
Borsuk — Ulam theorem 274
Boundary of a chain 248
Boundary of a set 123
Boundary set 124
Bounded function 111
Bounded space 110
Bounded, uniformly 110
Branch of a logarithm 258
Brouwer theorem 238
Cantor set 183
Cantor theorem 73 165 171
Cantor — Bendixson Theorem 162
Cantor — Bernstein theorem 75
cardinal number see Power
Cartesian product 40 55 109
Cartesian product of metric spaces 109
Cauchy sequence 164
Chain 246
Characteristic function 58 72
Characteristic function of a sequence 211
Closed relation 130
Closed set 121
Closure of a set 116
Commutative group 244
Compact space 168
Complement of a set 30
Complete space 164
COMPLEX 247
Component 203
Condensation point 161
Conjunction 21
Connected set 197
Connected space 196
Connected space between sets 205
Constituant 35
Continuity of a function at a point 131
Continuous convergence 176
Continuous function 131 132
Continuous mapping 131 174 180
Continuous ordering 84
Continuum 207
Continuum Hypothesis 93
Continuum, power of the 68
Convergent sequence 57 112 120
Coordinate axes 50
Coset 245
Countable set 62
Countably additive family of sets 54
Countably multiplicative family of sets 54
Critical number 100
Cutting of a space 257
Cycles 249
Cycles homologous to each other 251
Cycles homologous to zero in a complex 249
Cycles, homologously independent 251
Darboux property 200
De Morgan formulas (laws), for propositions 22
De Morgan formulas (laws), for propositions (generalized) 38
De Morgan formulas (laws), for sets 31
De Morgan formulas (laws), for sets (generalized) 49
Dedekind cut 84
Dense in itself set 125
Dense ordering 83
Dense set 124
Derived set 120
Derived set of a transfinite order 163
Diagonal theorem 73
Diameter of a space 110
Difference axiom 32
Difference of ordinal numbers 100
Difference of sets 25
Dimension of a space 227
Disjoint sets 26
Disjunction 21
Distance between a point and a set 144
Distance between points 109
Distance between sets 152
Division of sets 35
Domain 47
Edge of a simplex 233
Eilenberg theorem 258
Element of a group 244
Element of a set 25
Empty set 26
Equality of powers 60
Equivalence of propositions 21
Equivalence relation 67
Equivalence set 67
Euclidean -space,  43 228
Euler characteristic 254
Euler — Poincar formula 254
Existence axiom 32
Existential quantifier 37
Exponentiation of cardinal numbers 70
Exponentiation of ordinal numbers 95
Extension of a continuous function 146
Face of a simplex 233
Factor group see Quotient group
Family of additive sets 52
Family of Borel sets 55
First category set 165
Fixed point theorem 238
Frchet space 152
Function of two variables 41
Gauss plane 256
General principle of choice 96
Generalized cartesian product 55
Generalized de Morgan formulas 38 49
| Generalized operations 48
Greatest lower bound of a sequence of sets 57
Hausdorff space 129
Heine theorem 176
Hilbert cube 111
Hilbert space 110
Homeomorphic spaces 135
Homeomorphism 135
Homologous cycles 251
Homologously independent cycles 251
Homology group 251
Homomorphism 246
Homotopic functions 241
Image of a set 51
Implication 23
inclusion 28
Induction, transfinite 88
Infinite sequence 48
Infinitely countable set 62
Initial interval 83
Interior of a set 123
Intersection of sets 25
Inverse function 59 134
Inverse image 51
Isolated point 119
Isomorphism of groups 246
Janiszewski theorems 268
Jordan theorem 269
Kappa mapping 243
Kernel of a homomorphism 246
Lattice 85
Least upper bound of a sequence of sets 57
Least upper bound of an ordered set 84
Limit of a sequence of points 112 120
Limit ordinal number 95
Lindel f theorem 155
Linearly independent cycles 251
Linearly independent points 232
Local arcwise connectedness 217
Local connectedness 214
Local separability 163
Mbius band 253
Mapping of  onto  47
Mazurkiewicz Theorem 221
Mazurkiewicz — Moore theorem 221
Metric space 109
Mono tonic family of sets 85
Multiplicative family of sets 52
Negation 22
Neighborhood of a point 112 124 129
Neighborhood of a set 124
Neighborhood retract 150
Normal space 145
Nowhere dense set 125
Null set 26
One-to-one function (mapping) 59 134
Open set 121
Order type 82
Ordered pair 39
Ordered set 82
Ordering relation 81
Ordinal number 87
Ordinate 50
Ordinate axis 50
Oriented simplex 246
Partial function 51
Partial ordering 85
Partially ordered set 85
Peano theorem 222
Perfect set 126
Power 60
Power of cardinal numbers see Exponentiation of cardinal numbers
Power of ordinal numbers 95
Power of the continuum 68
Product of cardinal numbers 68
Product of order types 94
Product of propositions 21
Product of sets, Cartesian 40
Product of sets, set-theoretic 25
Projection of a set 50
Projective plane 253
Proper subset 28
Propositional function 36
Propositional function of variables 43
Quantifier 37
Quasi-component 205
Quotient group 245
Quotient of a set and a relation 67
Quotient of ordinal numbers 100
Quotient of sets 35
RANGE 47
Rank 273
Region 256
Relation 41 48
Relative boundary 129
Relative closure 128
Relative interior 129
Relatively closed set 128
Relatively dense set 85
Relatively open set 128
Retract of a space 150
Retricted function 51
Riesz theorem 173
Ring 34
Russell antinomy 74
Scattered set 126
Separable space 154
Separated sets 197
Separation of the space 257
Sierpi ski theorem 218
Similar orderings 81
Similarity mapping 81
simplex 232
Simplex, oriented 246
Simplicial mapping 255
Simplicial subdivision 233
Simply connected region 275
Sperner theorem 234
Spherical neighborhood 112
Subbase 130
Subgroup 245
Subset 28
Subtractive family of sets 53
Sum of cardinal numbers 68
Sum of order types 94
Sum of propositions 21
Sum, set-theoretic (of sets) 25
Symmetric difference of propositions 24
Symmetric difference of sets 34
Term of a sequence 48
Tietze extension theorem 147
Tihonov theorem 191
Topological invariants 103
Topological space 118
topology 103
Totally bounded space 191
Transfinite induction 88
Transfinite sequence 100
Triangle inequality 109
Trichotomy 91
Unicoherent space 274
Uniform continuity of a function 43 175
Uniform convergence 44 139
Uniformly bounded 110
Union axiom 32
Union of sets 25
Uniqueness axiom 32
Universal quantifier 37
Urysohn theorem 159
Value of a function 47
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