Point-Finite And Locally Finite Coverings

1. Introduction. An interesting feature of recent topological developments is the increasingly important role played by locally finite coverings. Point-finite coverings, on the other hand, even though conceptually simpler, have received very little attention. And deservedly so, since they are much less useful. Nevertheless, it sometimes happens (as it did to the author in (5)) that one is confronted by a covering which is known to be point-finite, but not necessarily locally finite.