Nets were firstly used to study convergence. Then, filters were introduced by Bourbaki as an alternative to nets. Nowadays, filters play a crucial role in different areas of mathematics. In this project we will focus only in more classical applications of nets and filters. More concretely, we aim to study sequential spaces using nets and to characterize elementary topological properties using filters. Nets are a generalization of sequences and consequently, a better tool to study convergence. It turns out that in a sense, filters and nets are equivalent. On the other hand, filters provide us a powerful tool to studytopological properties. One remarkable example is a (very) simple proof of the important Tychonoff theorem using the language of filters.
Obs! För GU-studenter räknas projektet som ett projekt i Matematik (MMG900/MMG910).
Examinator Marina Axelson-Fisk
Institution Matematiska vetenskaper