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Hausdorff compactifications. (English) Zbl 1505.54039

The authors show that each Hausdorff compactification of a Tychonoff space \(X\) can be obtained as a quotient of \(^*X\) where \(^*X\) is a \(\kappa\)-saturated nonstandard extension of \(X\), such that \(\kappa\) is greater than the cardinality of the topology of \(X\), endowed with the natural topology. They give applications to moduli spaces and potential theory.

MSC:

54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
03H05 Nonstandard models in mathematics
54J05 Nonstandard topology
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References:

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