1.basic set theory
1.1 inclusion
1.2 operation on sets
1.3 partially ordered sets and lattices
1.4 functions
1.5 relations;Cartesian products
2. cardinal numbers
2.1 countable numbers
2.1 countable Sets
2.2 cardinal numbers
2.3 comparison of cardinal number;Zorn's lemma
2.4 cardinal addition
2.5 cardinal multiplication
2.6 cardinal exponentiation
3. well-ordering;the axiom of choice
3.1 well-ordered sets
3.2 ordinal numbers
3.3 the axiom of choice
3.4 the continuum problem
4.basic properties of metric spaces
4.1 definitions and examples
4.2 open Sets
4.3 convergence;closed sets
4.4 continuity
5.completeness,separability,and compactness
5.1 completeness
5.2 separability
5.3 compactness
6.additional topics
6.1 product spaces
6.2 a fixed-point theorem
6.3 category
appendixes
1.examples of metric spaces
2.set theory and algebra
3.the transition to topological Spaces
· · · · · · (收起)