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Algebraic structures with additional non-algebraic structure

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description: 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: ...

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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Algebraic structures with additional non-algebraic structure

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