  (Write-up of a talk at the Bialowieza meeting, July 2007.)
  Gelfand and Kolmogorov in 1939 proved that a compact Hausdorff topological
space $X$ can be canonically embedded into the infinite-dimensional vector
space $C(X)^* $, the dual space of the algebra of continuous functions $C(X)$
as an "algebraic variety" specified by an infinite system of quadratic
equations.
  Buchstaber and Rees have recently extended this to all symmetric powers
$\Sym^n(X)$ using their notion of the Frobenius $n$-homomorphisms.
  We give a simplification and a further extension of this theory, which is
based, rather unexpectedly, on results from super linear lgebra.
