CW complex with closure finiteness and weak topology

Depends on

• Cell attachment by a characteristic map

Used by

• A weakly contractible CW complex is contractible Corollary
• Finite-CW real bundles have orthogonal complements under AC Corollary
• A cell decomposition without the weak topology need not be a CW complex Counterexample
• The Hawaiian earring is not a CW complex with its punctured circles as cells Counterexample
• The tautological line over RP∞ has no finite-rank complement Counterexample
• Based cellular chains of a universal cover as finite free right group-ring modules Definition
• Elementary expansions and collapses of finite CW complexes Definition
• Serre filtration over the base skeleta Definition
• Skeleta, CW subcomplexes, and relative CW complexes Definition
• Stiefel spaces, Grassmannians, and tautological bundles Definition
• A point and projective-line check of source-first convolution and opposite composition Example
• A torus translation has zero Lefschetz number and no fixed points Example
• Equivariant Ext of a point is degreewise finite and not total finite Example
• Unequal-dimensional proper pushforwards carry the summed-dimension Ext/Borel–Moore degree Example
• A closed smooth manifold has the homotopy type of a finite CW complex Lemma
• A compact C¹ leaf has finitely generated fundamental group Lemma
• A compact subspace of a CW complex meets only finitely many cells Lemma
• A curvilinear triangulation gives a finite regular CW complex Lemma
• A geodesically convex cover has the homotopy type of its nerve Lemma
• A low-dimensional disk can be pushed off a higher cell Lemma
• Based loop spaces of CW complexes have CW homotopy type Lemma
• Cellular attachments with finite boundary support form a CW complex Lemma
• Cellular mapping cylinders and relative cylinders are CW complexes Lemma
• Compact CW images have finite cell support without choice Lemma
• Compactified unstable manifolds give the Morse--Smale CW decomposition Lemma
• Finite cellulations of compact C² subsurfaces relative to an embedded graph Lemma
• Finite CW complexes are Euclidean neighborhood retracts Lemma
• Finite dimensional axiomatic homology has finite subcomplex support Lemma
• General linear frame spaces have the Stiefel cohomology gap Lemma
• General linear Stiefel approximations stabilize bounded constructible Hom Lemma
• Homotopy excision for a single relative cell layer Lemma
• Oriented real two-plane splitting with real-cohomology injection Lemma
• Planar facial graph facts and isomorphism extension for arbitrary arc drawings Lemma
• Smooth manifolds have CW homotopy type Lemma
• The Alexander module of a link complement is finitely presented Lemma
• The basepoint evaluation of the Stiefel section space is a fibration Lemma
• The complement of an oriented link is a connected smooth three-manifold Lemma
• The cyclic cover retracts onto the lifted flower and has a deck-equivariant spine model Lemma
• The Davis complex as a CW complex: disk cells and the Cayley skeleta Lemma
• The rational homology of a closed smooth manifold is finite-dimensional in each degree Lemma

…and 11 more results.

Dependency tree · one level

1 result within one dependency step of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• Allen Hatcher, Algebraic Topology, Chapter 0 (standard reference, not scraped)