MTH525 
Topology
 
TTh 12:30-1:45 PM
Lippitt Hall 201

Instructor    Araceli Bonifant  
Office: Lippitt Hall 202 G
Phone: 874-4394
Email: bonifant@uri.edu

Office Hours:

Book: Basic Topology by M. A. Armstrong

Course Description. Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. In this course we will cover a variety of different techniques and applications involving point set, geometric and algebraic topology. We will cover the first five or six chapters of the text.

Prerequisites. MTH435 or permission of instructor.


Tentative List of Topics:

  • Introduction: Euler's theorem, Topological equivalence, Surfaces, Abstract spaces, A classification theorem, Topological invariants.

  • Continuity: Open and closed sets, Continuous functions, A space-filling curve, The Tietz extension theorem.

  • Compactness and Connectedness: Closed bounded subsets of ${\mathbb E}^n$, The Heine-Borel theorem, Properties of compact spaces, Product spaces, Connectedness, Joining points by paths.

  • Identification spaces: Constructing a M\"obius strip, The identification topology, Topological groups, Orbit spaces.

  • The Fundamental Group: Homotopic maps, Construction of the fundamental group, Calculations, Homotopy type, The Brouwer fixed-point theorem, Separation of the plane, The boundary of a surface.

  • TBD:

    • Evaluation Policy:

  • Homeworks and Quizzes             25%
  • Exam I                                         20 %    Thursday October 13
  • Exam II                                         20 %    Thursday November 17
  • Final Exam                                     35 %     Thursday December 15        11:30 am - 2:30 pm

    • Standards of behaviour: Students are responsible for being familiar with and adhering to the published "Community Standards of Behavior: University Policies and Regulations" which can be accessed in the University Student Handbook. If you must come in late, please do not disrupt the class. Please turn off all cell phones, pagers, or any electronic devices.

    Special Accommodations: Any student with a documented disability is welcome to contact me as early in the semester as possible so that we may arrange reasonable accommodations. As part of this process, please be in touch with Disability Services for Students Office at 330 Memorial Union, 401-874-2098.