MATH 451 Topology

Prof. Dr. Kenan TaÅŸ

Course Description:

Introduction;  Sets, Relations, Ordering, Partial Ordering, Topological Spaces; definitions, accumulation points, closure of a set, interior, exterior and boundary, convergent sequences, coarser and finer topologies, Bases and subbases; topologies generated by classes of sets, Continuity and Topological Equivalence; Continuous functions, continuity at a point, sequential continuity at a point, closed and open functions; homeomorphisms; Countability; countability axioms; hereditary properties, Separation axioms; T1 -spaces Hausdorff spaces, Regular spaces, normal spaces, Urysohn's lemma, completely regular spaces, Compactness; covers, compactness and Hausdorff spaces, sequentially compact sets, local compactness, Product and quotient topologies; Connectedness; Complete metric spaces, Cauchy sequences, Function spaces, uniform convergence, C[0,1], equicontinuity, Ascoli’s theorem, compact open topology; Nets and Filters 

References:

  1. An Introduction to  General Topology, Paul E. Long
  2. Topology, James Munkres
  3. General Topology, J.L. Kelley,
  4. Introduction to Topology, Bert Mendelson
  5. General Topology, Seymour Lipchutz (Schaum's outline series)