Paracompact space

Definition
A topological space is said to be paracompact if it satisfies the following condition: every open cover has a locally finite open refinement.

Metaproperties
A paracompact space can have non-paracompact subspaces.

Any closed subspace of a paracompact space is paracompact.

Effect of property modifiers
Although a product of paracompact spaces need not be paracompact, there is a subclass of paracompact spaces with which the product of any paracompact space is paracompact. Such spaces are termed product-transitively paracompact; all compact spaces are product-transitively paracompact.

Textbook references

 * , Page 253 (formal definition)
 * , Page 148 (formal definition)