CW implies paracompact

This article gives the statement and possibly, proof, of an implication relation between two topological space properties. That is, it states that every topological space satisfying the first topological space property must also satisfy the second topological space property
View all topological space property implications | View all topological space property non-implications
|

Property "Page" (as page type) with input value "{{{stronger}}}" contains invalid characters or is incomplete and therefore can cause unexpected results during a query or annotation process.Property "Page" (as page type) with input value "{{{weaker}}}" contains invalid characters or is incomplete and therefore can cause unexpected results during a query or annotation process.

This article involves a proof using cellular induction, viz, it inductive construction on the $n$-skeleton of a cellular space

Statement

Any CW-space (viz a space that admits a CW-complex structure) is paracompact -- viz every open cover has a locally finite open refinement.

References

• Topology of CW complexes by A. T. Lundell and S. Weingram, P. 54