# Is this Wikipedia article linking to the wrong notion of coherent space

I'm reading up on infinite generalizations of the fundamental theorem of distributive lattices. Wikipedia (June 15, 2017) says that there is a duality

between distributive lattices and coherent spaces (sometimes called spectral spaces)

where I have reproduced the links as they appear. I think that the article on coherent spaces they have linked to is referring to a different, unrelated notion. Could someone in logic check me on this before I correct it?

Thanks, and apologies if this is too frivolous a use of MO.

• I'm not a logician but it seems wrong to me. Coherent space, as defined in Johnstone's book, means a topological space where the quasi-compact open sets form a distributive lattice and a basis for the topology. Jun 15 '17 at 15:25
• Doesn't seem frivolous to me. Jun 15 '17 at 15:25
• Aren't distributive lattices the Ind-completion of finite distributive lattices which are dual to finite posets = finite $T_0$ spaces (ncatlab.org/nlab/show/distributive+lattice#OppositeCategory)? Making the dual of distributive lattices the Pro-completion of finite $T_0$-spaces which is one description given at spectral space? Jun 15 '17 at 16:17