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Turing Award winner Juris Hartmanis introduced in 1959 lattices of subspacesof generalized partitions ("partitions of type n"; "geometries" if $n = 2$).Hartmanis states it is "an unsolved problem whether there are any incompletelattice homomorphisms in" lattices of subspaces of geometries. (He continues,"[I]f so how can these geometries be characterized.") We give a positive answerto this question.

On incomplete lattice homomorphisms in subspaces of geometries: "half" a problem of Hartmanis from 1959