Geodesic
Homomorphism-Compact Spaces
Canadian journal of mathematics, Tome 35 (1983) no. 3, pp. 558-576

Voir la notice de l'article provenant de la source Cambridge University Press

In 1979 Edgar asked for a characterization of those completely regular Hausdorff topological spaces X which have the property that any Boolean σ-homomorphism from the Baire σ-field of X into the measure algebra of an arbitrary complete probability space can be realized by a measurable point-mapping. Those spaces X will be called homomorphism-compact or, for short, H-compact hereafter. It is wellknown that compact spaces are H-compact (cf. [4], p. 637, Proposition 3.4). We will show that the same is true for strongly measure compact spaces. On the other hand H-compact spaces are easily seen to be real-compact. Since the notions of measure-compactness and liftingcompactness (cf. [3]) also lie between strong measure-compactness and real-compactness it is natural to investigate the relations among these notions. Here the results are mainly negative (cf. Sections 4 and 6). Concerning the structural properties of H-compactness not very much can be said so far (cf. Section 7): it is, for instance, unknown whether the product of two H-compact spaces is again H-compact. 
Babiker, A. G. A. G.; Graf, S. Homomorphism-Compact Spaces. Canadian journal of mathematics, Tome 35 (1983) no. 3, pp. 558-576. doi: 10.4153/CJM-1983-032-4
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