CW Pairs: Homotopy Extension Property

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Elementary Properties of Model Categories

Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.

Contracting Subspaces

Explores the homotopy extension property for contractable subspaces and their quotient maps.

Homotopic Extension Problem

Explores solving the homotopic extension problem, constructing relative CW complexes, and ensuring uniqueness in CW approximations.

Serre model structure on Top

Explores the Serre model structure on Top, focusing on right and left homotopy.

Homotopy Theory: Cylinders and Path Objects

Covers cylinders, path objects, and homotopy in model categories.

Model Categories: Properties and Structures

Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.

Fubini's Rule for Pushouts

Explores the Fubini Rule for pushouts, emphasizing the importance of transforming diagrams for maintaining pushout properties.

Homotopy Extension Property

Introduces the homotopy extension property, exploring conditions for extending continuous maps.

Group Actions: Quotients and Homomorphisms

Discusses group actions, quotients, and homomorphisms, emphasizing practical implications for various groups and the construction of complex projective spaces.

Serre model structure: Left and right homotopy

Explores the Serre model structure, focusing on left and right homotopy equivalences.