Coverings versus entourages (Q1379782)

Discussing several metrization theorems, the authors demonstrate the connections between the covering approach and the entourage method. In particular the Arkhangel'skij-Stone, Collins-Roscoe and Frink Metrization Theorems are shown to be equivalent to the Morita `Double-Star' Metrization Theorem. Furthermore they survey a range of uniform concepts generated by entourages, which characterize a wide variety of generalized metric properties.