Espaços quase-banach e resultados estruturantes

Abstract

This text studies fundamental concepts and structures in topological vector spaces, focusing on locally convex and quasi-normed spaces. The latter has a structure similar to normed spaces but generally is not a locally convex environment. Throughout the text, we explore the relevant aspects of the investigated environments and highlight their importance through structuring results. We investigate F-spaces from various perspectives and present classical results from the theory of Banach spaces in this context. Overview notions of the concepts of bases in topological vector spaces are studied, particularly the relationship between the extension of linear functionals and local convexity, usually known as the Hahn-Banach Extension Property (HBEP).