Editing Algebraic structure (section)

== Hybrid structures ==

Algebraic structures can also coexist with added structure of non-algebraic nature, such as [[Partially ordered set#Formal definition|partial order]] or a [[topology]]. The added structure must be compatible, in some sense, with the algebraic structure.

* [[Topological group]]: a group with a topology compatible with the group operation.
* [[Lie group]]: a topological group with a compatible smooth [[manifold]] structure.
* [[Ordered group]]s, [[ordered ring]]s and [[ordered field]]s: each type of structure with a compatible [[partial order]].
* [[Archimedean group]]: a linearly ordered group for which the [[Archimedean property]] holds.
* [[Topological vector space]]: a vector space whose ''M'' has a compatible topology.
* [[Normed vector space]]: a vector space with a compatible [[norm (mathematics)|norm]]. If such a space is [[complete metric space|complete]] (as a metric space) then it is called a [[Banach space]].
* [[Hilbert space]]: an inner product space over the real or complex numbers whose inner product gives rise to a Banach space structure.
* [[Vertex operator algebra]]
* [[Von Neumann algebra]]: a *-algebra of operators on a Hilbert space equipped with the [[weak operator topology]].