Notes on algebras and vector spaces of functions

TL;DR

This paper discusses different types of function spaces, such as continuous and holomorphic functions, across various mathematical contexts, providing insights into their algebraic and vector space structures.

Contribution

It offers an overview of algebraic and vector space properties of function spaces in diverse mathematical settings, emphasizing their structural aspects.

Findings

Characterization of function spaces as algebras and vector spaces

Analysis of continuous and holomorphic function spaces

Insights into structural properties of various function spaces

Abstract

These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.