relatively rightly compact

Definition

A subset K of a topological space X is called relatively rightly compact in X if whenever U is a locally finite collection of open subsets of X, K meets at most finite members of U.

Reference

Shou Lin, Zhangyong Cai, and Chuan Liu, The closed mappings on k-semistratifiable spaces, Houston J. Math. Vol.35 No.1 (2009).