Introduction to General Topology

• Grant number: 14/05102-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2014
• End date: December 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alexandre Paiva Barreto
• Grantee: Lino Chiozzini Neto
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 12/24454-8 - Algebraic, geometric and differential topology, AP.TEM

Abstract

The General Topology has as its central object of study the continuous functions between topological spaces. Unlike what was seen by the student in the courses of Differential Calculus, the notion of continuous function in this context makes absolutely set-theoretic, in other words, without a metric involved. This paradigm shift is extremely aggrandizing for the beginner mathematician since introduces, possibly for the first time, the power of abstraction and generalization of concepts. In this project we are interested not only in making a separate study of General Topology, but also in understanding, through applications, the relationships between this and the under graduation matters already attended by the student (in particular the Differential Calculus).