Cardinal Functions: Dominating Pairs, Pinning Down Pairs and Strogly Discretely Lindelöf spaces.

• Grant number: 25/08845-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2025
• End date: August 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Gabriel Zanetti Nunes Fernandes
• Grantee: João Marcelo Maciel Messias
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project aims to provide an introduction to the study of cardinal functions and the relations betweentopological spaces and their invariant cardinals. Over the 12 months of the project, we willstudy the introductory concepts of the subject, such as the main inequalities between invariantcardinals, later results on domination by small sets, asin (GRUENHAGE; TKACHUK; WILSON, 2020), exponential density of topologicalsubspaces, as in (BELLA; TKACHUK, 2021) and pinning down pairs in topologicalspaces, as in (JUHáSZ; SOUKUP; SZENTMIKLóSSY, 2020).Then we will see the results on cardinal functions presented in (BELLA;SPADARO, 2024) as well as discuss with the supervisor the open questionsof this article whose central theme is to modify strongly discreteLindelöf spaces so that they are worth strong characterizations. (AU)