compact with respect to the topology τ

定義

• For a bitopological space (X,τ_1,τ_2), the topology τ_i is compact with respect to the topology τ_j if for every i-open covering U of X and for each point x \in X there is a j-neighborhood of x covered by a finite subfamily of U.

出典

• Dvalishvili, B. P.,Bitopological spaces: theory, relations with generalized algebraic structures,and applications,North-Holland Mathematics Studies, 199. Elsevier Science B.V., Amsterdam, 2005.