MATH 451 Topology

Prof. Dr. Kenan Taş

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 propertiesSeparation axioms; T-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 


  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)