Radon-Nikodym compact

Definition

A compact Hausdorff space X is said to be Radon-Nikodym compact if there exists a lower semicontinuous metric with the following property: For every nonempty subset A of X and every positive number ε, there exists an open set U which meets A with radius less than ε.

Remark

• It is also called RN compact

Reference

Klaas Pieter Hart, Jun-iti Nagata and Jerry E. Vaughan, Encyclopedia of general topology, Elsevier Science Publishers, B.V., Amsterdam, 2004.