strongly open F_σ set

Definition

An open collection β of a topological space X is called an open complementary system if for every B in β, there exists a sequence {B_n} in β such that B coinsides with the union of the complements of B_n. A subset U of a topological space X is called a strongly open F_σ set if there exists a countable open complementary system β which includes U. The complement of a strongly open F_σ set is called a strongly closed G_δ set.

Reference

J. K. Hohli and D. Singh, Between compactness and quasicompactness, Acta. Math. Hungar. 106 (4) (2005), 317-329.