Difference between revisions of "Math 553: Foundations of Topology 1"

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=== Prerequisite ===
=== Prerequisite ===
Mth 451 or instructor's consent
=== Description ===
=== Description ===

Revision as of 10:29, 15 November 2012

Catalog Information


Foundations of Topology 1.

(Credit Hours:Lecture Hours:Lab Hours)





Mth 451 or instructor's consent


Naive set theory, topological spaces, product spaces, subspaces, continuous functions, connectedness, compactness, countability, separation axioms, metrization, and complete metric spaces.

Desired Learning Outcomes

Students should gain a familiarity with the general topology that is used throughout mathematics.

Minimal learning outcomes

  1. Set Theory
    • Finite, countable, and uncountable sets
    • Well-ordered sets
  2. Topological Spaces
    • Basis for a topology
    • Product topology
    • Metric topology
  3. Continuous Functions
  4. Connectedness
  5. Compactness
    • Tychonoff Theorem
  6. Countability and Separation Axioms
    • Countable basis
    • Countable dense subsets
    • Normal spaces
    • Urysohn Lemma
    • Tietze Extension Theorem
  7. Metrization
    • Urysohn Metrization Theorem
  8. Complete Metric Spaces


Possible textbooks for this course include (but are not limited to):

Additional topics

Paracompactness, the Nagata-Smirnov Metrization Theorem, Ascoli's Theorem, Baire Spaces and dimension theory as time allows.

Courses for which this course is prerequisite

Math 554