Courses

Metric spaces. Definition of metric space. Examples. Basic concepts of metric spaces (Open sets, Closed sets, Boundary of a set). Topological spaces. Definition of topology and examples of topological spaces. Various methods of determining topology. Basic concepts of topological spaces (closed case, interior, derivative, boundary). Subspace. Base and subbase of topology. Separability axioms. T0, T1, Hausdorff, Normal, Fully normal and Natural spaces. Moore-Smith mappings and sequences. Continuous mappings. Homomorphisms and examples. Moore - Smith convergence. Product of topological spaces. Product of finite and infinite number of topological spaces. Properties of the product of topological spaces. Universal spaces. Compact spaces. Compact spaces, Continuous mappings of compact spaces. Examples of compact spaces. Locally compact spaces. Compactification. Connected spaces. Connected spaces, Continuous mappings of connected spaces, Examples of connected spaces. Connected components. Locally connected spaces. Connected spaces along paths.