Potential Quiz Questions for Math 453, Fall 2004

Week Potential quiz questions
FOR IN-CLASS QUIZ
to be given on Monday, 9/6
(from classes 8/27 - 9/3)

Be ready to give a complete and precise definition of the following terms:
a countably infinite set
an indexed family of sets
the Cartesian product (of a family of sets indexed either by a finite set or by Z^+)
an n-tuple or an omega-tuple
an order relation

FOR IN-CLASS QUIZ
to be given on Monday, 9/13
(from classes 9/6 - 9/10)

Be ready to give a complete and precise definition of the following terms:
a topology on a set
a basis for a topology on a set
the topology generated by a basis
courser/finer/comparable topologies
the discrete topology on a set

FOR IN-CLASS QUIZ
to be given on Monday, 9/20
(from classes 9/13 - 9/17)

Be ready to give a complete and precise definition of the following terms:
subbasis
the topology generated by a subbasis
the product topology
the subspace topology
convex set

FOR IN-CLASS QUIZ
to be given on Monday, 9/27
(from classes 9/20 - 9/24)

Be ready to give a complete and precise definition of the following terms:
Hausdorff
continuous
continuous at a point
closure
limit point

FOR IN-CLASS QUIZ
to be given on Monday, 10/4
(from classes 9/27 - 10/1)

Be ready to give a complete and precise definition of the following terms:
homeomorphism
embedding
box topology
product topology (on a generalized Cartesian product)
metrizable

FOR IN-CLASS QUIZ
to be given on Monday, 10/18
(from classes 10/4 - 10/15)

Be ready to give a complete and precise definition of the following terms:
connected
retraction (from homework assignment)
quotient topology
quotient map
separation

FOR IN-CLASS QUIZ
to be given on Monday, 11/1
(from classes 10/18 - 10/29)

Be ready to give a complete and precise definition of the following terms:
path connected
locally connected
locally path connected
compact
(connected) component

FOR IN-CLASS QUIZ
to be given on Monday, 11/8
(from classes 11/1 - 11/5)

Prove the following theorem:
Every compact subspace of a Hausdorff space is closed.

FOR IN-CLASS QUIZ
to be given on Monday, 11/15
(from classes 11/8 - 11/12)

Be ready to give a complete and precise definition of the following terms:
1-point compactification
2nd countable
separable
regular
normal

LAST IN-CLASS QUIZ
to be given on Monday, 11/22
(from classes 11/15 - 11/19)

Be ready to give a complete and precise definition of the following terms:
homotopy
homotopy rel endpoints ("path homotopy" in Munkres)
fundamental group
homomorphism
isomorphism