Abstract:The closures of the pre-images associated with families of mappings in different topologies of normed spaces are considered. The question of finding a description of these closures by means of families of the same kind as original ones is studied. It is shown that for the case of the weak topology this question may be reduced to finding an appropriate closure of a given family. There are discussed various situations when the description may be obtained for the case of the strong topology. An example of a family is constructed which shows that it is, in general, impossible to find such a description for this case.
Keywords: closure, pre-image, mappings
AMS Subject Classification: 49J45, 49J20