τ-completely paracompact

Definition

Let τ denote an infinite cardinal number.
A cover λ of a topological space is called τ-star if, for any A in λ, St(A,λ) has a cardinality less than τ.
A topological space X is said to be τ-completely paracompact if any open cover of X has a σ-τ-star open weak refinement (that is, a refinement which can be represented as a countable union of open
covers that are τ-star refinements of the given cover).

Reference

D. K. Musaev, Uniformly superparacompact, completely paracompact, and strongly paracompact uniform spaces, J. Math. Sci., Vol.144, No.3, 2007