digraph G {
"Abelian Groups" -> "Modules" [dir=back];
"Abelian Groups" -> "Rings" [dir=back];
"Abelian Groups" -> "Vector Spaces" [dir=back];
"Algebras" -> "Lie Algebras" [dir=back];
"Algebras" -> "Tensor Algebras" [dir=back];
"Algebras" -> "Modules"
"Affine Spaces" -> "Vector Spaces" [dir=back];
"Affine Spaces" -> "Projective Spaces" [dir=back];
"Algebraic Varieties" -> "Topological Spaces"
"Affine Varieties" -> "Algebraic Varieties"
"Algebraic Groups" -> "Algebraic Varieties"
"Algebraic Groups" -> "Groups"
"Abelian Varieties" -> "Algebraic Groups"
"Abelian Varieties" -> "Projective Algebraic Varieties"
"Banach Algebras" -> "Banach Spaces"
"Banach Algebras" -> "Algebras"
"Projective Algebraic Varieties" -> "Algebraic Varieties"
"Linear Algebraic Varieties" -> "Algebraic Groups"
"Banach Spaces" -> "Hilbert Spaces" [dir=back];
"Bialgebras" -> "Algebras"
"Bialgebras" -> "Coalgebras"
"Hopf Algebras" -> "Bialgebras"
"Clifford Algebras" -> "Geometric Algebras" [dir=back];
"Euclidean Domains" -> "Fields" [dir=back];
"Fields" -> "Vector Spaces" [dir=back];
"Groups" -> "Abelian Groups" [dir=back];
"Groups" -> "Topological Groups" [dir=back];
"Groups" -> "Torsors";
"Group Rings" -> "Modules"
"Group Rings" -> "Rings"
"Inner Product Spaces" -> "Hilbert Spaces" [dir=back];
"Integral Domains" -> "UFDs" [dir=back];
"Lie Groups" -> "Lie Algebras" [dir=back];
"Loops" -> "Groups" [dir=back];
"Magmas" -> "Quasigroups" [dir=back];
"Magmas" -> "Semigroups" [dir=back];
"Measurable Spaces" -> "Measure Spaces" [dir=back];
"Measure Spaces" -> "Probability Spaces" [dir=back];
"Metric Spaces" -> "Topological Manifolds" [dir=back];
"Metric Spaces" -> "Riemannian Manifolds" [dir=back];
"Modules" -> "Vector Spaces" [dir=back];
"Monoids" -> "Groups" [dir=back];
"Monoids" -> "Rings" [dir=back];
"Normed Spaces" -> "Banach Spaces" [dir=back];
"Normed Spaces" -> "Inner Product Spaces" [dir=back];
"PIDs" -> "Euclidean Domains" [dir=back];
"Posets" -> "Lattices" [dir=back];
"Quasigroups" -> "Loops" [dir=back];
"Rings" -> "Integral Domains" [dir=back];
"Rings" -> "Modules" [dir=back];
"Semigroups" -> "Monoids" [dir=back];
"C^* Algebras" -> "Algebras"
"Symmetric Algebras" -> "Tensor Algebras"
"Sets" -> "Magmas" [dir=back];
"Sets" -> "Measurable Spaces" [dir=back];
"Sets" -> "Posets" [dir=back];
"Sets" -> "Topological Spaces" [dir=back];
"Schemes" -> "Algebraic Varieties"
"Smooth Manifolds" -> "Riemannian Manifolds" [dir=back];
"Smooth Manifolds" -> "Lie Groups" [dir=back];
"Tensor Algebras" -> "Clifford Algebras" [dir=back];
"Tensor Algebras" -> "Exterior Algebras" [dir=back];
"Topological Spaces" -> "Measure Spaces" [dir=back];
"Topological Spaces" -> "Metric Spaces" [dir=back];
"Metric Spaces" -> "Normed Spaces" [dir=back];
"Topological Spaces" -> "Topological Groups" [dir=back];
"Topological Spaces" -> "Topological Vector Spaces" [dir=back];
"Topological Spaces" -> "Uniform Spaces" [dir=back];
"Topological Spaces" -> "Projective Spaces" [dir=back];
"Topological Manifolds" -> "Smooth Manifolds" [dir=back];
"Topological Groups" -> "Lie Groups" [dir=back];
"Topological Vector Spaces" -> "Banach Spaces" [dir=back];
"Topological Rings" -> "Topological Groups"
"Topological Rings" -> "Rings"
"UFDs" -> "PIDs" [dir=back];
"Topological Groups" -> "Uniform Spaces" [dir=back];
"Topological Vector Spaces" -> "Uniform Spaces"
"Vector Spaces" -> "Normed Spaces" [dir=back];
"Vector Spaces" -> "Topological Vector Spaces" [dir=back];
}