L2

This course provides a rigorous yet accessible introduction to the fundamental concepts of general topology, with an emphasis on metric and topological spaces commonly encountered in analysis. Beginning with a review of distances and norms, the course develops core notions such as open and closed sets, closure, interior, boundary, and neighborhoods. Key topological properties—including continuity (in its topological formulation), convergence of sequences, compactness, and connectedness—are explored in depth. Through a variety of examples and counterexamples drawn from real analysis and elementary geometry, students build both intuition and formal reasoning skills. The course aims to lay a solid foundation for advanced studies in real and functional analysis, geometry, and dynamical systems.