## Real Analysis Exchange

### Representation of abstract affine functions.

Jiří Spurný

#### Abstract

It is known that any subspace $\H$ of the space of continuous functions on a compact set can be represented as the space of affine continuous functions defined on the state space of $\H$. The aim of this paper is to generalize this result for abstract affine functions of various descriptive classes (Borel, Baire etc.). The important step in the proof is to derive results on the preservation of the descriptive properties of topological spaces under perfect mappings. The main results are applied on the space of affine functions on compact convex sets and on approximation of semicontinuous and Baire--one abstract affine functions.

#### Article information

Source
Real Anal. Exchange, Volume 28, Number 2 (2002), 337-354.

Dates
First available in Project Euclid: 20 July 2007

https://projecteuclid.org/euclid.rae/1184963799

Mathematical Reviews number (MathSciNet)
MR2009758

Zentralblatt MATH identifier
1057.46005

#### Citation

Spurný, Jiří. Representation of abstract affine functions. Real Anal. Exchange 28 (2002), no. 2, 337--354. https://projecteuclid.org/euclid.rae/1184963799

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