strongly compact with respect to the topology τ

定義

• For a bitopological space (X,τ_1,τ_2) the topology τ_i is　strongly compact with respect to the topology τ_j if τ_i is compact with respect to τ_j　and for every point x \in X there is a j-open i-extendable neighborhood U(x) such that U(x) \subset U_{Ｕ(x)} for every i-open covering Ｕ of X, i-extended from U(x).

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.