WEEK 9  
M: Closed sets and normal functions. 
     1.75. Definition. Limit point of a set. 
     1.76. Definition. Closed set, closed class, set closed in \alpha.  
     1.77. Remark. Interval topology on ordinals. 
     1.78. Definition. Normal function. 
     1.79. Proposition. Closed sets are images of normal functions.
     1.80. Definition. Successor cardinals, limit cardinals. Cardinal successor of an ordinal.
     1.81. Remark. Successror cardinals can be expressed as \alpha+ where \alpha is a cardinal  
     1.82. Corollary. The function \aleph is normal.
W: Cardinality. Basic cardinal arithmetic.
     1.83. Proposition. A set is equinumerous to a cardinal iff it is well-orderable.
     1.84. Definition. Cardinality.
     1.84a. Definition. Cardinal addition and multiplication.
     1.84b. Remark. Basic properties of cardinal addition and multiplication.
     1.85. Definition. Maximo-lexicographic ordering.  
     1.86. Proposition. Maximo-lexicographic ordering induced by a well-ordering is a well-ordering.
     1.87. Theorem. If \kappa is an infinite cardinal then \kappa ×  \kappa ~ \kappa.
     1.88. Corollary. (a) if m,n are natural numbers, cardinal addition/multiplication
                                       corresponds to ordinal addition/multiplication.
                                  (b) if m,n are non-zero and at least one of them is infinite then
                                       m + n = m · n = max{m,n}.  
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