There are many examples of mathematical structures where algebraic structure exists alongside non-algebraic structure. Topological vector spaces are vector spaces with a compatible topology. Lie groups: These are topological manifolds that also carry a compatible group structure. Ordered groups, ordered rings and ordered fields have algebraic structure compatible with an order on the set. Von Neumann algebras: these are *-algebras on a Hilbert space which are equipped with the weak operator topology. |

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