Lectures related to Numerical Analysis and Optimization: Concepts of Distance and Subsets

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Explores boundaries in sets, defining them as points not well separated from the set or its complement.

Explores interior points, boundaries, adherence, and compact sets, including definitions and examples.

Explores open sets, compactness, and connectivity in topology, covering topological spaces and compact sets.

Covers the concept of quotient spaces and the quotient topology, defining open sets and characterizing functions.

Introduces real analysis basics, including functions, sequences, limits, and set properties in R.

Explores free abelian groups, homomorphisms, and exact sequences in the context of different categories.

Covers absolute value, density of rationals, and real line topology.