The next 16 of February, at 12:00 h (Barcelona time), I will conduct a Talk in the Informal Seminar of Mathematics of Barcelona (SIMBa) about the changes in the filter definition that have occurred the past years, because of the formalization of mathematics through theorem provers. Below you can see the title and the abstract of the talk.

Title: From far-out mystery to a useful tool

Abstract: This talk aims to redefine topological filters in order to obtain a helpful tool that can be used to prove some propositions in topology using semiring theory. In this talk, we will see the first definition of filters provided by Henri Cartan, which is used to define limits in general topological spaces, and we will state some famous theorems about filters and topology. Changing the definition slightly allows us to prove some propositions by using group theory identities, we will show this by solving some topology-undergraduate problems as trivial algebraic identities.

If you wish to see the official talk sheet, it can be seen in SIMBa_sheet.