| Popis: |
If C p ( X ) is jointly metrizable on compacta, then p ( X ) ≤ ω but ω 1 need not be a caliber of X. If X is either submetrizable or a P-space, then C p ( C p ( X ) ) is jointly metrizable on compacta and, in particular, all compact subsets of C p ( C p ( X ) ) are metrizable. We show that for any dyadic compact X, the space C p ( X ) is jointly metrizable on compacta. Therefore, the JCM property of C p ( X ) for a compact space X does not imply that X is separable. If X is a compact space of countable tightness and C p ( X ) is jointly metrizable on compacta, then it is independent of ZFC whether X must be separable. |
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