Accumulation point 179
Annulus 144
Antipodal point 130
Arc component 143
Archimedean principle 103
Arcwise connected 139
Basis for closed sets 70
Basis for neighborhoods 66 94 114
Basis for open sets 55 67 113 175
Bolzano — Weierstrass property 183 186 190
Borsuk — Ulam theorem 132
Boundary 101
Bounded 170 171 177
Cartesian product 13
Cauchy sequence 185
Closed 2-manifold 207
Closed interval 5
Closed set 60 88
Closure 96
Closure space 98
Commutative field 2
Compact 164 165
Compactum 178
Complement 8
Complete linearly ordered field 3
Complete metric space 185
Complete system of neighborhoods 46 89 94
Completely separable 191
Component 135
Composition of functions 20 43
Connected 117
Constant function 18 41 120
Constant path 153
continuous 40 103
Contractible to a point 161
Countable 187
Covering 163
Covering, finite 163
Covering, open 164
Crosscap 208
Curve 139
Cylinder 198
de Morgan’s laws 8 11
Deleted neighborhood 180
Dense 103 192
Denumerable 187
Diagram 21 22
Diagram, commutative 22
Direct product 13
Disc 155 195 196
Discrete 85
Distance function 33
Distance, between a point and a subset 63
Domain of a function 16
Equivalence relation 150
Equivalence set 151
Euclidean n-space 14 85
Extension of a function 29 148
Finite intersection property 171
First axiom of countability 50 192
Fixed-point theorem 126 128
Function 16 103
Graph of a function 16
Greatest lower bound 62
Ham-sandwich problem 132
Hausdorff space 90 168 169 170
Hausdorff, axiom 50 90
Homeomorphism 106
Homotopic 147
Homotopy class 153
Identification topology 194
Identity function 18 41
Image 16
Imbedding 121
Inclusion mapping 30 111
Indexed family 10
Initial point 139
Interior 100
Intermediate Value Theorem 125
Intersection 7 10
interval 122
| Inverse functions 26
Inverse image 16
Invertible 26
Isolated point 180
Klein bottle 202
Least upper bound 3
Lebesque number 182
LIMIT 56 57
Lindeloef’s theorem 191
Linearly ordered 3
Locally compact 178
Locally connected 137
Loop 140
Lower bound 62
Mapping 17
Metric space 33
Metrically equivalent 76
Moebius strip 199
Monotone increasing 44
Mutually disjoint 102
n-sphere 72
n-tuple 14
Natural numbers 1
Neighborhood 45 87
Neighborhood space 91
Null set 5
One-one 18
One-point compactification 178
Onto 18
Open interval 5
Open mapping 104
Open set 4 52 86
Open sphere 45
Ordered pair 13
Orientable 208
Partition 136
Path 139
Path, closed 140
Product of topological spaces 113
Projection first 19
Projection i-th 59 115
Projection second 19
Projective plane 207
Range of a function 16
Rational density theorem 103 192
Real line 85
refinement 192
Reflexive 150
Relative neighborhood 109
Relative topology 109
Relatively closed 110
Relatively open 108
Restriction of a function 29
retract 161
Retraction 130
Schwarz’s lemma 82
Second axiom of countability 191
Separable 192
Simply connected 154
Sub-base 70
Subcovering 164
Subset 5
Subset improper 5
Subset proper 5
subspace 71 108 199
Surface symbol 207
symmetric 150
Terminal point 139
Topological property 119 167
Topological space 4 84
Topological space, associated with a metric space 85 110
Topological space, metrizable 86
Topologically equivalent 78
topology 84
Torus 201
Transformation 17
Transitive 150
Underlying set 33 84
Uniformly continuous 184
union 7 10
Unit n-cube 72 128 177
Upper bound 3
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