The notion of continuous symmetry has largely and successfully been formalised in the mathematical notions of topological group, Lie group and group action. For most practical purposes, continuous symmetry is modelled by a group action of a topological group that preserves some structure. Particularly, let f : X → → Y be a function, and G is a group that acts on X ; then a subgroup H ⊆ ⊆ G is a symmetry of f if f ( h ⋅ ⋅ x ) = f ( x ) for all h ∈ ∈ H .