TIES676 COM2: Baire's theorem and some of its consequences (2-3 op)

Arvosteluasteikko

Hyväksytty-hylätty

Opetuskieli/-kielet

englanti

Osaamistavoitteet

Baire's category theorem

Suoritustavat

Lectures and exercises.

Sisältö

In this course, we discuss Baire's category theorem, that is, roughly speaking, a complete metric space is thick in a certain sense. We provide corollaries thereof, such as the closed graph theorem or the open mapping theorem. We will further prove that the algebraic dimension of an infinite dimensional Banach space is necessarily uncountable. The results have also implications for numerical analysis.

Arviointiperusteet

Obligatory attendance at lectures and completing the exercises.

Esitietovaatimukset

Basic knowledge of Banach spaces