Metric spaces: Definition of metric space. Examples. Basic notions of metric spaces (Open sets, Closed sets, Boundary of a set).
Topological spaces: Definition of topology and examples of topological spaces. Various methods to appoint topology. Basic notions of topological spaces (closure, interior, derivative, boundary). Subspace, Base and subbase of topology.
Separation axioms: T₀, T₁, Hausdorff, Regular, Completely regular and Normal spaces.
Functions and Moore-Smith sequences: Continuous functions, Homomorphisms and examples. Moore-Smith Convergence.
Product of topological spaces: Product of finite and infinite family of topological spaces. Properties of product of topological spaces. Universal spaces.
Compact spaces: Compact spaces. Continuous functions of compact spaces. Examples of compact spaces. Locally compact spaces. Compactification.
Connected spaces: Connected spaces. Continuous functions of connected spaces. Examples of connected spaces. Connected components. Locally connected spaces. Path connected spaces.