Supercompact space

Definition
A topological space is termed supercompact if it has a subbasis such that any open cover of the topological space whose elements come from the subbasis, has a subcover comprising at most two members.

Stronger properties

 * Compact metrizable space
 * Compact linearly orderable space

Weaker properties

 * Compact space:

Metaproperties
An arbitrary product of supercompact spaces is supercompact, in the product topology.