CW complex

CW-复形

Geometry & Topology · Graduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: cell complex

Translation evidence: Literature usage

Meaning in context

A space built by attaching disks to successive skeleta along their boundary spheres and giving the union the weak topology determined by the skeleta.

逐层把闭球的边界粘到低维骨架上，并给最终并集赋予由骨架决定的弱拓扑所形成的空间。

Example

SnS^n has a CW structure with one zero-cell and one n-cell.

Usage and distinctions

A finite-dimensional CW complex can have infinitely many cells; finite-dimensional and finite are different conditions.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Allen Hatcher — Algebraic TopologyChapter 0, Cell Complexes, printed pp. 5–7; Appendix, Topology of Cell Complexes · Checked 2026-10-14

Translation sources

  1. UCAS — 代数拓扑 course syllabus第一章第4节 CW-复形；第二章 CW-复形的同伦性质 · Checked 2026-10-14
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