Ostaszewski, Adam 
ORCID: 0000-0003-2630-8663
(2011)
Analytically heavy spaces: analytic cantor and analytic Baire theorems.
Topology and its Applications, 158 (3).
pp. 253-275.
ISSN 0166-8641
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: | 11 Sep 2025 08:00 |
| URI: | http://eprints.lse.ac.uk/id/eprint/33382 |
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