Generalizations of compactness

• Grant number: 15/26326-5
• Support Opportunities: Scholarships in Brazil - Master
• Start date: July 01, 2016
• End date: February 28, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Lúcia Renato Junqueira
• Grantee: Rodrigo Rey Carvalho
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The topic proposed in this project is about generalizations of compactness in topological spaces with the goal of developing aspects in the area of set theory, as for instance small cardinals and infinite combinatorics. Another goal is to understand examples and study recent results obtained in this area. The main properties that will be studied are, among others,sequential compactness, countable compactness and Lindelof property. We will analise, in particular, the behavior of these properties with respect to product, for example the Scarborough-Stone problem. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

CARVALHO, Rodrigo Rey. The Scarborough-Stone problem. 2018. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.