Some remarks on Radon--Nikodým compact spaces (Q2773376)

The author defines the notion of a ``quasi Radon-Nikodym'' compact space, a generalization of a Radon-Nikodym compact space, introduced independently by Reinov and Namioka, through the use of a quasi-metric in place of the metric in Namioka's characterization of R-N compact spaces. He shows that quasi R-N spaces generalize results of various authors concerning R-N spaces, establishes conditions under which quasi R-N spaces are actually R-N, and notes relationships of commonality between these spaces and the ones described as ``scattered''. Finally, an embedding theorem for totally disconnected quasi R-N spaces in the space of regular Borel measures is proved.NEWLINENEWLINENEWLINE(Note: The author remarks that it was pointed out by Namioka that the quasi R-N spaces are exactly those defined earlier as ``strongly fragmented'' in a paper by Arkhangelskij).