|245||Chapter 5 Outline|
Sections, concepts, and problems
Section 1. Relations.
Relations from one set to another, domain, range, diagonal relations on a
set, reflexive relations, symmetric relations, transitive relations,
antisymmetric relations, Cartesian and directed graphs of relations (the
latter done in class)
Section 2. Equivalence Relations.
Equivalence relations, equivalence classes, partitions, congruence modulo
Section 3. Partial Orders.
Posets, total/linear ordered sets and some of their properties,
maximum element, maximal elements, mimimum element, minimal elements,
upper bounds, least upper bound (supremum), lower bounds, greatest lower
bound (infimum), complete posets, subposets
Section 4. Quotient Spaces.
Quotient spaces and three applications: identification spaces in topology
(not in book), quasiorders and quotient spaces, and algebraic structures
and quotient spaces.