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                                Course Syllabus for Math 445
 

                                                   VIRGINIA STATE UNIVERSITY
                            SCHOOL OF AGRICULTURE, SCIENCE AND TECHNOLOGY
                                                  DEPARTMENT OF MATHEMATICS
                                               MATH 445  - Topology - 3 sem. hours

                                                   COURSE SYLLABUS: SPRING 2001
 

COURSE DESCRIPTION:

Metric spaces, topological spaces, continuous functions and homeomorphisms, compactness, connectedness, separation axioms and product spaces.

Prerequisites: MATH 425 or MATH 300

COURSE TEXT:
C. Wayne Patty; Foundations of Topology, Waveland Press, Inc., 1997, P. O. Box 400 Prospect Heights, Il. 60070
 

TOPICS TO BE COVERED:

  1. Topological Spaces
    • Metric Spaces
    • Topological Spaces
    • Basis for a Topology
    • Closed Sets, Closures, and Interiors and Example
    • Convergence, Continous Functions and Homeomorphisms
  2. New Spaces from Old Ones
    • SuspacesThe Product Topology on X x Y
    • The Product Topology and the Weak Topology
    • The Uniform Metric
    • Quotient Spaces
  3. Connectness
    • Connected Spaces
    • Pathwise and Local Connectedness
    • Totally Disconnected Spaces
  4. Compactness
    • Comactness in Metric Spaces
    • Compact Spaces
    • Local Compactness
  5. The Separation and Countability Axiom


GRADING STANDARDS:

The student will be evaluated on:

                                            Class tests         400
   Comprehensive mid-term examination       100
         Comprehensive final examination        200
          Home assignments and quizzes            200
          One special Research topic of
           student's choice                                  100
                                   Total                        1000 points
 

Letter Grade:
                        A   90 - 100
                        B    80 - 89
                        C    70 - 79
                        D    60 - 69
                        F     below 59
 

BIBLIOGRAPHY/READING LIST

Besides the textbook, listed below are some books which students should consult for their reference and further development.  Remember that these are not the only books on topology.  There are plenty more in the University library.

Hocking, John G. (1961) Topology, Addison-Wesley Publishing Company, Inc., Reading, Massachusetts.

Sharma, J. N. (1995) Topology, Krishna Prakashan Mandir, Meerut - India.

Long, Paul E. (1971) An Introduction to General Topology, Charles E. Merrill Publishing Company, Columbus, Ohio.

Kelley, John L. (1967) General Topology, D. Van Nostrand Company, Inc., Princeton, New Jersey.

Sims, Benjamin T., (1976) Fundamentals  of  Topology, MacMillan Publishing Co., Inc. New York.

Mendelson, Bert, (1968) Introduction to Topology, Allyn and Bacon, Inc., Boston, Massachusetts.

Cain, George L. (1994) Introduction to General Topology, Addison-Wesley Publishing Company, Reading, Massachusetts.

Patty, Wayne C., (1993) Foundations of Topology PWS-Kent Publishing Company, Boston, Massachusetts.

Munkres, James R., (1974) Topology, A first Course. Prentice-Hall College Division.

Gamelin, Theodore W. & Greene, Robert E., (1999) Intoduction to Topology. Dover Publications.