An elementary nonstandard proof of Stone's representation theorem
Brunet, Bernard
Illinois J. Math., Tome 35 (1991) no. 4, p. 312-315 / Harvested from Project Euclid
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A neat nonstandard proof of Stone's representation theorem is given. Improving on previous proofs (Loeb [5], Brunet [2]), it uses the remarkably simple fact that infinitesimal members of a filter on $X$, in any enlargement, are always compact for a natural topology on ${}^{\ast}X$.
Publié le : 1991-06-15
Classification:  46E10,  03H05,  46E30,  46S20,  54J05 
@article{1255987899,
     author = {Brunet, Bernard},
     title = {An elementary nonstandard proof of Stone's representation theorem},
     journal = {Illinois J. Math.},
     volume = {35},
     number = {4},
     year = {1991},
     pages = { 312-315},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255987899}
}

Brunet, Bernard. An elementary nonstandard proof of Stone's representation theorem. Illinois J. Math., Tome 35 (1991) no. 4, pp.  312-315. http://gdmltest.u-ga.fr/item/1255987899/