Concept

Quotient space (topology)

Related lectures (32)

Explores the identification of the space SO(3) and the topology of SS-space of R₃(R).

Covers quotient spaces, combinatorial groups, generators, and coatings of surfaces.

Topology: Exploring Cohomology and Quotient Spaces

Covers the basics of topology, focusing on cohomology and quotient spaces, emphasizing their definitions and properties through examples and exercises.

Quotient by a Relation

Covers the concept of quotient space by a relation and its applications.

Inverse Limits and Topologies

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

Recognizing a Quotient

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

Quotient Topology

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

Modular curves: Riemann surfaces and transition maps

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.

Proper Actions and Quotients

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Homogeneous Spaces and Quotients

Covers homogeneous spaces, group actions, and separating quotient spaces in mathematics.

Homotopy and Quotient Spaces

Covers homotopy, quotient spaces, and the universal property in topology.

Local structure of totally disconnected locally compact groups V

Explores the local structure of totally disconnected locally compact groups, focusing on GER and Mon (G), their properties, and faithful actions.

Topology: Separation Criteria and Quotient Spaces

Discusses separation criteria and quotient spaces in topology, emphasizing their applications and theoretical foundations.

Haar Measures and Quotient Functions

Covers Haar measures, quotient functions, and their importance in group actions.

Topology: Homotopy and Projective Spaces

Discusses homotopy, projective spaces, and the universal property of quotient spaces in topology.

Wedge: Family of Spaces

Explores the concept of a wedge of spaces and explicit parainization.

Quotient Spaces: Three Ways

Explores three ways to form quotient spaces using group actions and equivalence relations.

Topology: Compactness and Continuity

Explores compactness, continuity, and quotient spaces in topology, emphasizing the topology of lines in R² and the properties of compact sets.

Orbit Spaces

Explores the concept of orbit spaces and group actions in topological spaces, including translations and multiplications.

Properties of X/G

Explores the properties of the quotient space X/G when X is compact and sometimes separated.