The course has seven chapters:
Fundamental definitions and properties (open and closed sets, neighborhoods, convergent sequences).
Bases, sub-bases and local bases (fundamental neighborhoods)(fundaments of a topology).
Continuous Functions (global, local, and sequential continuity) and equivalent topological spaces.
Countability (working with sequences) and separation (unique limits).
Compactness (open cover and extraction of a finite subcover) (Alexander's theorem and Heine-Borel theorem, properties, compactness in R^{n}) and sequential compactness (extraction of a convergent subsequence).
Product spaces (product topology, Tychonoff's product compactness theorem).
Metric spaces (metric topology, compactness in metric spaces (compactness equivalent to sequential compactness), complete metric spaces (compact = closed and totally bounded).
