Lectures related to Quotient by a Relation

Explores inverse limits, profinite completions, and Hausdorff topologies in group theory and topology.

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Discusses the recognition of a quotient in topology and the properties of the quotient topology.

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Explores quotients of groups by equivalence relations and the conditions for well-defined sets.

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

Explores upgrading foundations from embedded to general manifolds in optimization, discussing smooth sets and tangent vectors.

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Discusses well pointed spaces, neighborhoods, wedges, examples, and the universal property of the quotient.