M.A.D. families in topology

• Grant number: 15/15166-7
• Support Opportunities: Scholarships in Brazil - Master
• Start date: January 01, 2016
• End date: December 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Artur Hideyuki Tomita
• Grantee: Vinicius de Oliveira Rodrigues
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The student will study techniques and results about almost disjoint families and psi spaces in his Master, taking as starting point the surveys by Alan Dow and Michael Hrusak in the Recent Progress in Topology III (2014), in order to learn new important techniques to his development to researcher, producing a dissertation on the matter in the end. An almost disjoint family (on omega) is a collection of infinite subsets (of omega) such that the intersection of any two distinct members of the collection is finite. A Psi space is a topological space associated in a natural way with an almost disjoint family which is used to answer a variety of contemporary questions in general topology. The topological properties of the psi spaces depend on the combinatorial properties of the almost disjoint families that generated them, and the set theoretical techniques and infinite combinatorics applied to build almost disjoint families with sophisticated properties are also used to solve many other problems in general topology. (AU)

Academic Publications

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

RODRIGUES, Vinicius de Oliveira. Almost disjoint families in topology. 2017. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.