Brauner space

In functional analysis and related areas of mathematics a Brauner space is a complete compactly generated locally convex space ${\displaystyle X}$ having a sequence of compact sets ${\displaystyle K_{n}}$ such that every other compact set ${\displaystyle T\subseteq X}$ is contained in some ${\displaystyle K_{n}}$.

Brauner spaces are named after Kalman George Brauner, who began their study. All Brauner spaces are stereotype and are in the stereotype duality relations with Fréchet spaces:

Special cases of Brauner spaces are Smith spaces.

In the special case when ${\displaystyle M=G}$ possesses a structure of a topological group the spaces ${\displaystyle {\mathcal {C}}^{\star }(G)}$, ${\displaystyle {\mathcal {E}}^{\star }(G)}$, ${\displaystyle {\mathcal {O}}^{\star }(G)}$ become natural examples of stereotype group algebras.