MATH 451 Topology

Prof. Dr. Kenan Taş

Course Description:

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 continuityat a point, closed and open functions; homeomorphisms; Metric Spaces; distance between sets,equivalent metrics, convergence and continuity in metric spaces, 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, Product and quotient topologies; Connectedness; Complete metric spaces, Cauchy sequences, Function spaces, uniform convergence, C[0,1], equicontinuity, Ascoli’s theorem, compact open topology.

References:

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