MATHEM ATICS 4300
GENERAL TOPOLOGY
MATH 4300: General Topology
Topology can be viewed in a number of ways, as a type of generalized geometry sometimes called rubber
sheet geometry, or as the study of continuity, though without the and familiar from analys
MATH 4300
General Topology
Time slot
20
Fall 2013
Section Classroom
001
HH 3017
Instructor: Dr. Eduardo Mart
nez-Pedroza
Email: [email protected] Oce: HH-3006.
Oce hours: Tuesdays and Thursdays from 2-3:30pm, Fridays 3-4pm.
Prerequisites of MATH 4300: M
MATH 4300
Test 1
MATH4300. General Topology.
Test 1.
Name:
1. (Interior, Closure, Boundary.) Let A and B be subsets of a topological space X.
(a) Show that A B A B.
(b) Provide an example where equality fails.
2. (Continuous Functions) Let X and Y be topo
MATH 4300
Quiz 1
MATH4300. General Topology.
Quiz 1.
Name:
There are 6 parts. Time: 30 minutes. Total number of marks: 25.
1. (5 marks) Examples.
Draw an illustration of S 1 R
Draw an illustration of S 1 S 1
Draw an illustration of an open set of R R with
MATH4300. General Topology.
Problem set 1.
1. (Intermediate Value Theorem) Let p(x) be a polynomial with integer coecients of odd degree. Show that the equation p(x) = 0 has at least one
real solution.
2. ( - Continuity) Recall that a subset U R is an ope
Distances
The distance between a point and a line
The distance between a point A and a line is the length of a shortest line segment AB such
that B lies on . B will be the point such that AB . How do we determine the
point B and the length of AB?
A
B
Let
MATH4300. General Topology.
Problem set 4.
1. Let D1 and D2 be two open disks in R2 whose closures D1 and D2 intersect
in exactly one point, so the boundary circles of the two disks are tangent.
Determine which of the following subspaces of R2 are connect
MATH4300. General Topology.
Problem set 3.
Submit solutions to six of the following eight problems.
1. Let O be the collection of all intervals Ia = (a, ) in R, including the
cases I = and I = R. Show that O denes a topology on R. In this
topology, what i
MATH4300. General Topology.
Problem set 2.
Recall that R denotes the set of real numbers with the standard topology,
and R denotes the set of real numbers with the lower limit topology, i.e the
topology generated by the basis consisting of half open inter
MATH4300. Problem Set 6. MATH6332 Problem Set 5.
MATH4300, solve ve of the following problems. MATH6332, solve all the
problems.
1. Connectedness and Path-Connectedness in R2
(a) Show that if U is an open connected subspace of R2 , then U is pathconnected