F-paracompact

Definition

A uniform space (X,U) is said to be F-paracompact if any open cover of this space has a σ-U-discrete (i.e., decomposable into a countable family of U-discrete subsystems) open refinement.

Remark

• Note that all metrizable and all R-paracompact spaces are B-paracompact, all B-paracompact spaces are F-paracompact.

Reference

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