Abstract
The intuitive notion of forming a compactification of a topological space is to “attach” new points to a space to “compactify” it. We use equivalence relations on the remote points of an enlargement of a given topological space to produce the new points. Thus, nonstandard methods are shown to unify the various extant approaches to compactification.
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Notes
- 1.
One might consider applying nonstandard methods to the notion of ends presented in [8], leading one to use enlargements of directed sets and nets. The first author looked at this briefly with Mr. Tom Cuchta, but preliminary investigations suggest that the resulting theory is essentially equivalent—at greater complexity cost—with the work in [7].
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Insall, M., Loeb, P.A., Marciniak, M.A. (2015). General and End Compactifications. In: Loeb, P., Wolff, M. (eds) Nonstandard Analysis for the Working Mathematician. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-7327-0_5
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DOI: https://doi.org/10.1007/978-94-017-7327-0_5
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