It is a pleasant fact that Stone-duality may be described very smoothly when restricted to the category of compact spectral spaces: The Stoneduals of these spaces, arithmetic algebraic lattices, may be replaced by their sublattices of compact elements thus discarding infinitary operations. We present a similar approach to describe the Stone-duals of coherent spaces, thus dropping the requirement of having a base of compact-opens (or, alternatively, replacing algebraicity of the lattices by… CONTINUE READING