R-paracompact

Definition

A uniform space X is called R-paracompact iff each open cover U of X admits a uniformly locally finite open refinement V, i.e. there exists a uniform cover, each of whose elements meets at most finitely many elements of V.

Remark

• [Rice1977]All R-paracompact spaces are complete.

Reference

• D. Buhagiar and T. Miwa, On superparacompact and Lindeloef GO-spaces, Houston J. Math. Vol.24, No.3, 1998.
• M. D. Rice, A note on uniform paracompactness, Proc. Amer. Math. Soc., 62, No.2, 359-392 (1977).
• D. K. Musaev, Uniformly superparacompact, completely paracompact, and strongly paracompact uniform spaces, J. Math. Sci., Vol.144, No.3, 2007