CW complex

A complex or cell CW complex is a mathematical object from the area of ​​algebraic topology. It is a generalization of the simplicial complex, and was introduced by John Henry Constantine Whitehead.

Definition

A cell is a topological space that is homeomorphic to. An open - cell is a topological space that is homeomorphic to the interior of. is called the dimension of the cell.

A cell complex or CW complex ( closure - finite weak- topology ) is a Hausdorff space which is divided into open cells, where:

Properties

Every CW - complex is normal, but does not necessarily satisfy the first axiom of countability, is not necessarily metrizable. Every CW - complex is locally contractible.

Examples

  • Every simplicial complex is a CW - complex.
  • CW is a complex. Consider the cells, and the characteristic images.

Cellular images

The skeleton of a CW - complex is the union of all its cells of dimension.

A CW - Figure ( or cellular imaging ) is a continuous mapping, the mapping of each cell in the skeleton of. (n- cells need not necessarily be mapped to n- cells. )

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