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Flashcards in Misc II Deck (66):
1

topology on X

61
3 properties

2

neighborhood of x

62

3

closed set

63

4

Hausdorff space

64

5

examples of topology

65

6

finer/coarser, topologies

66

7

subspace topology

67

8

interior of A

68

9

exterior of A

69

10

boundary of A

70

11

limit point of A

71

12

derived set of A

72

13

closure of A

73

14

basis of a topology

74
2 criteria

15

product topology on XxY

75

16

(dis)connected

76

17

how to identify connected spaces

77
3 of em

18

open covering

78

19

compact

79

20

Heine-Borel theorem

80

21

continuity in general

81

22

results for continuous maps

82
4 of em

23

open map

83

24

homeomorphic

84

25

supremum/infimum

85

26

Cauchy sequence

86

27

complete space

87

28

Lebesgue measure

88

29

Lebesgue measurable sets

89
3 of em

30

Lebesgue measurable function

90

31

step function

91

32

Lebesgue integral

92

33

completeness of L^p

93

34

complex numbers

94

35

complex conjugate

95

36

modulus of z

96

37

argument of z

97

38

Euler's formula

98

39

deMoivre's formula

99

40

nth roots of unity

100

41

nth roots of w

101

42

complex logarithm

102

43

complex powers

103

44

constant in complex

104

45

trigonometric functions, complex

105

46

hyperbolic cosine/sine

106

47

properties of sinh, cosh

107
8 of em

48

complex function differentiable at z0

108

49

Cauchy-Riemann equations

109

50

Laplace's equation

110

51

analytic

111

52

complex line integral

112

53

Cauchy's Theorem

113

54

Morera's Theorem

114

55

Cauchy's Integral Formulas

115

56

Cauchy's Derivative Estimates

116

57

Liouville's Theorem

117

58

The Maximum Principle

118

59

radius of convergence

119

60

punctured open disk

120

61

singularity

121

62

pole of order n

122

63

Laurent series

123

64

residue

124

65

iterative method

125

66

bisection method

126