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