Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9516691 | Topology and its Applications | 2005 | 15 Pages |
Abstract
We show that the dyadicity index can be increased by taking the square even in the class of second countable spaces. Besides, any compact group contains a dense subspace of dyadicity index zero. We prove that, for any infinite cardinal κ, a compact space K with Ï(x,K)⩾κ for any xâK cannot be represented as a union of ⩽κ-many subspaces of network weight <κ. This fact has quite a few interesting consequences when we consider mappings of function spaces onto compact spaces. We prove, in particular, that if K is an Ï1-monolithic Lindelöf Σ-space then every compact continuous image of Cp(K) is metrizable. For any cardinal κ an example is given of a compact space K such that Cp(K) maps continuously onto the Tychonoff cube of weight κ. We also establish that Luzin's axiom (2Ï1>c) is equivalent to metrizability of all compact continuous images of Cp(K) whenever K is a separable compact space.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
M.G. Tkachenko, V.V. Tkachuk,