Algebraic Structures With Additional Non-algebraic Structure
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.
Read more about this topic: Outline Of Algebraic Structures
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