Abstract
The division into skies and constellations of *N–N, the set of infinite numbers in a nonstandard model of arithmetic, was described in Puritz, of which this chapter is partly a continuation. The chapter summarizes the key results of the connected sky structure of an ultra power N N / μ with a classification of ultrafilters in a completely different context. The notion of a filter monad is of considerable use in the study of topology. The notion of a filter monad by Luxemburg and independently by Machover and Hirschfeld is also explained in the chapter. Conditions are described in which the image of a monad under a standard mapping is obtained. The chapter concludes with a discussion of the weak topology of Hilbert space, which is uniformisable.
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