• Let ${\displaystyle M}$  be a ${\displaystyle \sigma }$ -compact locally compact topological space, and ${\displaystyle {\mathcal {C}}(M)}$  the Fréchet space of all continuous functions on ${\displaystyle M}$  (with values in ${\displaystyle {\mathbb {R} }}$  or ${\displaystyle {\mathbb {C} }}$ ), endowed with the usual topology of uniform convergence on compact sets in ${\displaystyle M}$ . The dual space ${\displaystyle {\mathcal {C}}^{\star }(M)}$  of Radon measures with compact support on ${\displaystyle M}$  with the topology of uniform convergence on compact sets in ${\displaystyle {\mathcal {C}}(M)}$  is a Brauner space.
• Let ${\displaystyle M}$  be a smooth manifold, and ${\displaystyle {\mathcal {E}}(M)}$  the Fréchet space of all smooth functions on ${\displaystyle M}$  (with values in ${\displaystyle {\mathbb {R} }}$  or ${\displaystyle {\mathbb {C} }}$ ), endowed with the usual topology of uniform convergence with each derivative on compact sets in ${\displaystyle M}$ . The dual space ${\displaystyle {\mathcal {E}}^{\star }(M)}$  of distributions with compact support in ${\displaystyle M}$  with the topology of uniform convergence on bounded sets in ${\displaystyle {\mathcal {E}}(M)}$  is a Brauner space.
• Let ${\displaystyle M}$  be a Stein manifold and ${\displaystyle {\mathcal {O}}(M)}$  the Fréchet space of all holomorphic functions on ${\displaystyle M}$  with the usual topology of uniform convergence on compact sets in ${\displaystyle M}$ . The dual space ${\displaystyle {\mathcal {O}}^{\star }(M)}$  of analytic functionals on ${\displaystyle M}$  with the topology of uniform convergence on bounded sets in ${\displaystyle {\mathcal {O}}(M)}$  is a Brauner space.

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.

• Let ${\displaystyle M\subseteq {\mathbb {C} }^{n}}$  be a complex affine algebraic variety. The space ${\displaystyle {\mathcal {P}}(M)={\mathbb {C} }[x_{1},...,x_{n}]/\{f\in {\mathbb {C} }[x_{1},...,x_{n}]:\ f{\big |}_{M}=0\}}$  of polynomials (or regular functions) on ${\displaystyle M}$ , being endowed with the strongest locally convex topology, becomes a Brauner space. Its stereotype dual space ${\displaystyle {\mathcal {P}}^{\star }(M)}$  (of currents on ${\displaystyle M}$ ) is a Fréchet space. In the special case when ${\displaystyle M=G}$  is an affine algebraic group, ${\displaystyle {\mathcal {P}}^{\star }(G)}$  becomes an example of a stereotype group algebra.
• Let ${\displaystyle G}$  be a compactly generated Stein group.^[5] The space ${\displaystyle {\mathcal {O}}_{\exp }(G)}$  of all holomorphic functions of exponential type on ${\displaystyle G}$  is a Brauner space with respect to a natural topology.^[6]

• Stereotype space
• Smith space

• Brauner, K. (1973). "Duals of Fréchet spaces and a generalization of the Banach-Dieudonné theorem". Duke Mathematical Journal. 40 (4): 845–855. doi:10.1215/S0012-7094-73-04078-7.
• Akbarov, S.S. (2003). "Pontryagin duality in the theory of topological vector spaces and in topological algebra". Journal of Mathematical Sciences. 113 (2): 179–349. doi:10.1023/A:1020929201133. S2CID 115297067.
• Akbarov, S.S. (2009). "Holomorphic functions of exponential type and duality for Stein groups with algebraic connected component of identity". Journal of Mathematical Sciences. 162 (4): 459–586. arXiv:0806.3205. doi:10.1007/s10958-009-9646-1. S2CID 115153766.