Syllabus
• Scalar product, Inner product space, orthogonality
• Metric, metric space
• Norm, ed space
• Open and closed sets, interior, boundary and closure of a set
• Convergency, completeness
• Continuous mappings
• Examples of spaces of sequences and functions
Annotation
In the course, basic concepts from the theory of metric and normed spaces. Concepts as neighbourhood, convergence, metric, norm, complete metric space, compact space are dealt with.
The course offers a deeper and more general perspective on some parts of algebra and calculus. Understanding the topic on the base of examples is emphasized.