Ascoli Theorems and the Pseudocharacter of Mapping Spaces
The pseudocharacter of the space YX of continuous functions from X to Y is studied. For certain topologies on YX sufficient conditions, which are shown in some cases also to be necessary, for YXto have a specified pseudocharacter are given. An Ascoli theorem is a theorem which characterizes the compact subsets of YX. Several Ascoli theorems are obtained, including ones which utilize results on pseudocharacter.