Some topological consequences of the Product Measure Extension Axiom
For a Tychonoff space , we will denote by the set of its isolated points and will be equal to . The symbol denotes the space of real-valued continuous functions defined on . is the Cartesian product with its box topology, and is with the topology inherited from . By we denote the set can be continuously extended to all of . A space is almost--resolvable if it can be partitioned by a countable family of subsets in such a way that every non-empty open subset of has a non-empty...
In this paper, we prove the following statements: (1) For every regular uncountable cardinal , there exist a Tychonoff space and a subspace of such that is both relatively absolute star-Lindelöf and relative property (a) in and , but is not strongly relative star-Lindelöf in and is not star-Lindelöf. (2) There exist a Tychonoff space and a subspace of such that is strongly relative star-Lindelöf in (hence, relative star-Lindelöf), but is not absolutely relative star-Lindelöf...