## Illinois Journal of Mathematics

### An elementary nonstandard proof of Stone's representation theorem

Bernard Brunet

#### Abstract

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 ${}^{\ast}X$.

#### Article information

Source
Illinois J. Math., Volume 35, Issue 2 (1991), 312-315.

Dates
First available in Project Euclid: 19 October 2009

https://projecteuclid.org/euclid.ijm/1255987899

Digital Object Identifier
doi:10.1215/ijm/1255987899

Mathematical Reviews number (MathSciNet)
MR1091445

Zentralblatt MATH identifier
0714.46055

#### Citation

Brunet, Bernard. An elementary nonstandard proof of Stone's representation theorem. Illinois J. Math. 35 (1991), no. 2, 312--315. doi:10.1215/ijm/1255987899. https://projecteuclid.org/euclid.ijm/1255987899