finely paracompact

Definition

A topological space is called finely paracompact if any open cover has a locally finite open refinement consisting of arcwise connected sets.

Reference

Vladimir P. Okhezin, On the fixed-point theory for non-compact maps and spaces.I, Topological Methods in Nonlinear Analysis, Journal of the Juliusz Schauder Center, Volume 5, 1995, 83-100.