Syllabus:

General topology
 Topological structure in a set
 Metric spaces
 Subspaces of a topological space
 Continuous maps
 Homeomorphisms
 Connectedness
 Separation axioms
 Countability axioms
 Compactness
 Sequential compactness
 Product of topological spaces
 Quotient topology
 Fundamental group and coverings
 Homotopy
 Fundamental group and high homotopy groups
 Dependence of fundamental group on the base point
 Simplyconnectedness
 Coverings
 Calculations of fundamental group using universal coverings
 Behavior of fundamental group under a continuous map
 Classification of coverings
 CWcomplexes
 Applications of fundamental group
 Manifolds
 Topological manifolds
 Onedimensional manifolds
 Triangulated twodimensional manifolds
Students with Disabilities: If you have a physical,
psychological, medical, or learning disability that may impact on your
ability to carry out assigned course work, you are strongly urged to
contact the staff in the Disabled Student Services (DSS) office: Room
133 in the Humanities Building; 6326748v/TDD. The DSS office will
review your concerns and determine, with you, what accommodations are
necessary and appropriate. A written DSS recommendation should be
brought to your lecturer who will make a decision on what special
arrangements will be made. All information and documentation of
disability is confidential. Arrangements should be made early in the
semester so that your needs can be accommodated.