Function spaces jointly metrizable on compacta

[摘要] If C-p(X) is jointly metrizable on com.pacta, then p(X) <= omega but col 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. (C) 2015 Elsevier Inc. All rights reserved.

[发布日期] 2015-12-15

[关键词] Joint metrizability on compact subsets;JCM property;Caliber;Compact space;Dyadic space;P-space