Mad Families, Forcing and Combinatorial Principles in Topology

• Grant number: 17/15502-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: January 01, 2018
• End date: June 30, 2022
• 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
• Associated scholarship(s): 19/01388-9 - Set Theory: Forcing and its Iterations, BE.EP.DR

Abstract

This Ph.D. research project gives sequence to the applicant's Ms. project approved by FAPESP (2015/15166-7), with an end foreseen for 12/2017. We will study questions in topology regarding mad families, Mrówka spaces, relations between generalizations of compactness between a space X and its Vietoris hyperspace CL(X) and regarding generalizations of compactness in topological groups, where the last two topics are also part of the advisor's research project approved by FAPESP (2016/26216-8). The applicant has already studied several scientific publications about these topics and the research will have as a starting point the study of some open problems proposed by world experts in these subjects. The expected result is to achieve advances in these areas that can be evaluated from their dissemination (publications of scientific articles, seminars and conferences).

Scientific publications

(8)

(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)

BELLINI, MATHEUS KOVEROFF; RODRIGUES, VINICIUS DE OLIVEIRA; TOMITA, ARTUR HIDEYUKI. On countably compact group topologies without non-trivial convergent sequences on Q((kappa)) for arbitrarily large kappa and a selective ultrafilter. Topology and its Applications, v. 294, MAY 1 2021. (16/26216-8, 17/15502-2, 17/15709-6)

ORTIZ-CASTILLO, Y. F.; RODRIGUES, V. O.; TOMITA, A. H.. Small cardinals and the pseudocompactness of hyperspaces of subspaces of beta omega. Topology and its Applications, v. 246, p. 9-21, SEP 1 2018. (16/26216-8, 14/16955-2, 17/15502-2)

RODRIGUES, VINICIUS DE OLIVEIRA; TOMITA, ARTUR HIDEYUKI. Small MAD families whose Isbell-Mrowka space has pseudocompact hyperspace. FUNDAMENTA MATHEMATICAE, v. 247, n. 1, p. 99-108, 2019. (16/26216-8, 17/15502-2)

RODRIGUES, VINICIUS DE OLIVEIRA; RONCHIM, VICTOR DOS SANTOS; SZEPTYCKI, PAUL J.. Special sets of reals and weak forms of normality on Isbell-Mrowka spaces. COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, v. 64, n. 1, p. 18-pg., 2023-01-01. (17/15502-2)

BELLINI, MATHEUS K.; HART, KLAAS PIETER; RODRIGUES, VINICIUS O.; TOMITA, ARTUR H.. Countably compact group topologies on arbitrarily large free Abelian groups. Topology and its Applications, v. 333, p. 23-pg., 2023-04-28. (17/15502-2, 21/00177-4, 16/26216-8, 17/15709-6)

RODRIGUES, VINICIUS DE OLIVEIRA; RONCHIM, VICTOR DOS SANTOS. Almost-normality of Isbell-Mrowka spaces. Topology and its Applications, v. 288, FEB 1 2021. (17/15502-2)

BELLINI, MATHEUS KOVEROFF; BOERO, ANA CAROLINA; CASTRO-PEREIRA, IRENE; RODRIGUES, VINICIUS DE OLIVEIRA; TOMITA, ARTUR HIDEYUKI. Countably compact group topologies on non-torsion Abelian groups of size continuum with non-trivial convergent sequences. Topology and its Applications, v. 267, NOV 1 2019. (10/19272-2, 12/01490-9, 17/15709-6, 16/26216-8, 17/15502-2)

GUZMAN, O.; HRUSAK, M.; RODRIGUES, V. O.; TODORCEVIC, S.; TOMITA, A. H.. Maximal almost disjoint families and pseudocompactness of hyperspaces. Topology and its Applications, v. 305, JAN 1 2022. (19/01388-9, 17/15502-2, 19/19924-4)

Academic Publications

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

RODRIGUES, Vinicius de Oliveira. Weakenings of compactness and normality on Isbell-Mrówka spaces, Hyperspaces of Vietoris and Abelian groups. 2022. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.