Continuous selections and realcompactness
Continuous selections and realcompactness
The class of basically fixed, lowersemicontinuous carriersis defined, and the existence of continuous selections formembers of this class is investigated. It is shown that,barring the existence of measurable cardinals, a completelyregular Hausdorff space is realcompact iff every basicallyfixed, lowersemicontinuous carrier of infinite character fromthe space to the convex subsets of …