Ostaszewski, Adam (2011) Analytically heavy spaces: analytic cantor and analytic Baire theorems. Topology and its Applications, 158 (3). pp. 253-275. ISSN 0166-8641
Full text not available from this repository.Abstract
Motivated by recent work, we establish the Baire Theorem in the broad context afforded by weak forms of completeness implied by analyticity and,kappa-analyticity, thereby adding to the 'Baire space recognition literature' (cf. Aarts and Lutzer (1974) [1], Haworth and McCoy (1977) [43]). We extend a metric result of van Mill, obtaining a generalization of Oxtoby's weak alpha-favourability conditions (and therefrom variants of the Baire Theorem), in a form in which the principal role is played by kappa-analytic (in particular analytic) sets that are 'heavy' (everywhere large in the sense of some sigma-ideal). From this perspective fine-topology versions are derived, allowing a unified view of the Baire Theorem which embraces classical as well as generalized Gandy-Harrington topologies (including the Ellentuck topology), and also various separation theorems. A multiple-target form of the Choquet Banach-Mazur game is a primary tool, the key to which is a restatement of the Cantor Theorem, again in kappa-analytic form.
| Item Type: | Article |
|---|---|
| Official URL: | http://www.elsevier.com/wps/find/journaldescriptio... |
| Additional Information: | © 2011 Elsevier B.V. |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 20 Mar 2011 15:18 |
| Last Modified: | 05 Jan 2024 20:24 |
| URI: | http://eprints.lse.ac.uk/id/eprint/33382 |
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