"Closed" manifold 83
"Coherently" oriented triangles 102
 -curve (Theta-curve) 31
2-cell (two-cell), closed 36
2-dimensional (two-dimensional) manifold 83
Accessibility 27
Acyclic curve 33
Admissible representation 56
Agreement in orientation of triangles 102
Agreement in sense of traversals 63 104
Applications of modulus function 77
ARC 26
Arcwise connectedness 25
Basis 6
Binormal mapping 81
Borel theorem 6
Boundary curve (edge) 83
Boundary of a set 12
Boundary point 83
Branch 56
Brouwer Reduction Theorem 15
Cauchy sequence 22
Cauchy – Riemann equations 52
Chain of type T 16
Characteristic, Euler 98
Circulation index 58
Closed 2-cell 36
Closed set 4
Compact mapping 90
Compact set 5
Complementary domain 32
Complete enclosure 22
Complete space 22
COMPLEX 98
Complex number system 41
Complex plane 44
Component 10
Conditionally compact set 5
Connected set 9
Continuity of a function 50
Continuous branch 56
Continuous transformation 20
Continuum 12
Continuum generalized 12
Continuum irreducible 14
Continuum of convergence 13
Convergent sequence of sets 7
Countable set 3
Curve acyclic 33
Curve boundary 83
Curve level 77
Curve open 100
Curve simple closed 28
Curved simplex 98
Cut point 33
Cyclic set 34
Cyclicly connected set 33
Deficiency of a function 101
Degree of a function 90
Dense 5 93
Derivative 51
Diameter 7
Differentiability conditions 52
Disjoint sets 3
Distance between two sets 7
Distance function 3
Domain, complementary 32
E-chain (epsilon chain) 10
Edge point 83
Edges of a graph 67
Elementary region 38
Enumerable set 3
Euler characteristic 98
Exponential function 53
Exponential representation 56
Extension of openness 81
Extension of transformations 22
Fine subdivision 17
Frontier 12
Function, exponential 53
Function, logarithm 55
Function, meromorphic 92
Function, modulus 77
Function, power 88
Function, upper semi-continuous 6
Fundamental (Cauchy) sequence 22
Generalized continuum 12
Graph 67
Hexagonal subdivision 32
Homeomorphism 20
Homeomorphism, positive (negative) 64
Homotopy 68
Hurwitz theorem 93 110
Image 20
INDEX 58
Index invariance 64 68
Index near a non-zero of the derivative 72
Index, topological or circulation 58
Inducible (inductive) property 14
Inferior limit 7
Interior mapping 76
Invariance of agreement in sense 63
Invariance of index 64 68
Inverse 20
Irreducible continuum 14
Isolated point 80
Isometric 23
Isomorphic (similar) simple subdivisions 38
Jordan curve theorem 29
Level curve 77
Light mapping 75
Lightness of differentiable functions 75
Limit of a function 50
Limit point 4
Limit superior 7
Limit theorem 11
Limit, inferior 7
Lindeloef theorem 5
Local degree of a function 84 101
Local topological analysis 88
Locally compact set 5
Locally connected set 13
Locally topological mapping (local homeomorphism) 85
Logarithm function 55
m-fold zero of a function 93
Manifolds orientable and non-orientable 102
Manifolds with boundary 83
Manifolds, 2-dimensional 83
Manifolds, ordinary or "closed," 83
Manifolds, triangulation of 2-dimensional 102
Mapping theorems 24
Mappings compact 90
Mappings homotopic 68
Mappings light 75
Mappings locally topological 85
| Mappings modulus 77
Mappings monotone 25
Mappings normal and binormal 81
Mappings open (interior) 76
Mappings power 88
Mappings quasi-open 110
Mappings strongly open (strongly interior) 76
Mappings topologically equivalent 86
Maximum modulus theorem 77
Measure of the image of the zeros of the derivative 72
Meromorphic function 92
Metric 3
Metric spaces 3
Modulus function (mapping) 77
Monotone mapping 25
Mutually exclusive sets 9
Negative homeomorphism 64
Negative traversal 62
Neighborhood, Spherical 4
Non-dense set 93
Non-orientable manifolds 104
Normal mapping 81
One-to-one (1-1) transformation 20
Open (interior) mapping 76
Open mappings on simple cells and manifolds 86
Open set 4
Openness of differentiable functions 76
Openness, uniform 108
Order n, point of 35
Ordinary ("closed") manifold 83
Ordinary (regular) point 83
Orientability and orientation 101
Orientable 2-dimensional manifolds 102
Orientation agreement of triangles 102
Phragmen – Brouwer Theorem 32
Plane separation theorem 34
Point inverse of a 20
Point inverse, scattered 83
Point isolated 80
Point limit 4
Point of order n 35
Point regular 35
Point, cut 33
Point, edge (boundary or singular) 83
Polar form (of a complex number) 45
Pole of a function 92
Positive homeomorphism 64
Positive traversal 62
Power mapping 88
Powers and roots 46
Property S 16
Punctured complex plane 69
Quasi-open mapping 110
Reduced differentiability assumptions 93
Reduction Theorem, Brouwer 15
Region 15
Regular (ordinary) point 35
Rouchd Theorem 93
S-property 16
Scattered inverse property 83
Semi-polygon 30
Sense agreement of traversals 63 104
Separability 5
Separation 9
Sequence uniformly open 108
Sequence, Fundamental (Cauchy) 22
Sets boundary of (frontier of) 12
Sets closed 4
Sets compact 5
Sets complete 22
Sets complete enclosure of 22
Sets components of 10
Sets conditionally compact 5
Sets connected 9
Sets convergent collection of 7
Sets countable (enumerable) 3
Sets cyclic 33
Sets cyclicly connected 34
Sets disjoint (mutually exclusive) 3
Sets non-dense 93
Sets open 4
Sets well-chained 10
Sets, arcwise connected 26
Sets, dense 5 93
Sets, diameter of 7
Sets, distance between 7
Sets, locally compact 5
Sets, locally connected 15
Sets, operations on 3
Sets, subdivision of 36
Sets, uniformly locally connected 16
Similar (isomorphic) simple subdivisions 38
Similarity correspondence 38
Simple arc 26
Simple closed curve 28
Simplex, curved 98
Simplex, sides of a 98
Singular point 98
Space, complete 22
Space, metric 3
Space, topologically complete 22
Spherical neighborhood 4
Straight 0-, 1-, 2-dimensional 98
Strongly open (strongly interior) mapping 76
Subdivision Theorem 36
Subdivisions hexagonal 32
Subdivisions isomorphic simple 38
Subdivisions simple 37
Subdivisions simplicial 98
Subdivisions, fine 17
Superior limit 7
Topological index 56
Topological transformations 20
Topologically complete space 22
Topologically equivalent mapping 86
Torhorst Theorem 32
transform 20
Transformation 20
Traversal of arcs and simple closed curves 60
Traversal of region boundaries and region subdivisions 67
Traversal, positive 62
Traversals, agreement in sense of 63 104
Triangles, "coherently" oriented 102
Triangulation of 2-dimensional manifold 102
Type T Chain 16
Uniform openness 108
Uniformly continuous transformation 21
Uniformly locally connected set 16
Uniformly open sequence 108
Upper semi-continuous function 5
Vertices of a graph 67
Vertices of a simplex 98
Well-chained set 10
Zero sides (0-sides) of a simplex 98
Zoretti Theorem 35
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