Stone duality and Banach spaces C(K)

• Grant number: 11/01285-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2011
• End date: December 31, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Christina Brech
• Grantee: Clayton Suguio Hida
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this project we propose the study of the relation between properties of three kind of structures: Boolean algebras, compact topological spaces and Banach spaces. For this, we will study the duality between Boolean algebras and certain compact Hausdorff (the Stone duality) and the ``duality'' between compact Hausdorff spaces and Banach spaces C(K). As a consequence of those dualities, there are several corresponding properties of these objects, some of which we plan to study. The final purpose is to study a paper by R. Haydon, where he presents the construction of an interesting Banach space C(K), whose properties are obtained through the mentioned dualities.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

HIDA, CLAYTON SUGUIO. Two Cardinal inequalities about bidiscrete systems. Topology and its Applications, v. 212, p. 71-80, OCT 1 2016. (11/01285-3, 13/01609-9)