User:Jshflynn/Simmons Topology and Analysis

= Part One: Topology =

$\S 1$ Sets and Set Inclusion
Definition:Set

Definition:Element

Definition:Explicit Set Definition

Definition:Implicit Set Definition

Definition:Set Definition by Predicate

Definition:Open Real Interval

Definition:Half-Open Real Interval

Definition:Closed Real Interval

Definition:Universal Set

Definition:Finite Set

Definition:Infinite Set

Definition:Membership Relation

Definition:Set Equality

Definition:Subset

Definition:Superset

Definition:Proper Subset

Definition:Proper Superset

Definition:Conditional

Definition:Biconditional

Set is Subset of Itself

Equivalence of Definitions of Set Equality

Subset Relation is Transitive

Definition:Ordinary Set

Definition:Extraordinary Set

Russell's Paradox

Definition:Total Ordering

Definition:Partial Ordering

Subset Relation is Ordering

Cardinality of Power Set of Finite Set

Cardinality of Subset Relation on Power Set of Finite Set