Topological properties about open coverings and discrete subsets

• Grant number: 12/07124-4
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: October 01, 2012
• End date: October 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Lúcia Renato Junqueira
• Grantee: Lúcia Renato Junqueira
• Visiting researcher: Richard Gordon Wilson Roberts
• Visiting researcher institution: Universidad Autónoma Metropolitana, Iztapalapa (UAM Iztapalapa), Mexico
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

Prof. Wilson, Junqueira and Alas will investigate questions about star-covering, discretely generated (DG) and weakly discretely generated (WDG) spaces. These last two were introduced by Wilson et al. in 2002. They will work on several important problems on the topic, which includes: 1. Is the product of c+ copies of the reals star-countable? 2. What happens to perfect images and pre-images of star-P spaces? 3. Does exist in ZFC a compact Hausdorff (or even, just Hausdorff) space DG such that its square is not DG? 4. Extend the ordinal function idc for Cech-complete spaces and k-spaces. 5. Study different products of DG and WDG spaces. For instance, is radial times DG also DG? 6. Is there a Hausdorff WDG space with countable extent which is not DG? (AU)