Metric spaces

Lecturer: Pekka Alestalo (2017, 2018, 2019), Kalle Kytölä (2020)
Teaching assistant: Armando W. Gutiérrez

This is a six-week undergraduate-level course designed for students with a major in mathematics, applied mathematics, or physics.

Content:

• Real numbers
• Metric, norm, inner product
• Open and closed sets
• Continuous mappings
• Sequences and limits
• Compactness
• Completeness
• Connectedness

Study material:

• Carothers, N.L. Real analysis. Cambridge University Press, 2000
• Rudin, W. Principles of mathematical analysis. McGraw-Hill, 1976
• Väisälä, J. Topologia I. Limes ry, 1999