**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**; *T _{1 }*-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:**

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