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  "body": "\n## Summary\n\nA lattice with a least element is atomistic if every element is the join of the [[atoms|TTVCTW6TNC]] below it.\nSo the whole lattice is generated from its atoms by joins, as every subset of a set is the union of its one-element subsets.\nEvery atomistic lattice is [[atomic|5SE8EMSDNY]], but not conversely.\nGeometric lattices, such as the lattice of subspaces of a vector space, are atomistic.\n\n## Explanations\n\n### L1 human\n\nIn an atomistic lattice the atoms are building blocks, and every element is put together from the atoms it contains.\nIn the subsets of a set, every set is the union of its points.\nIn the subspaces of a finite-dimensional vector space, the atoms are the lines through the origin, and every subspace is spanned by the lines it contains.\nA chain $0 \u003c 1 \u003c 2$ is atomic but not atomistic: its only atom is $1$, and $2$ is not a join of atoms.\n",
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