The correspondence defines an inner product on the space of continuous functions on the interval I.

The Hamiltonian is not invariant under spatial diffeomorphisms and therefore its action can only be defined on the kinematic space.

The total variation is a norm defined on the space of measures of bounded variation.

Due to the lack of orientation, there is no boundary operator defined on the space of varifolds.

Any closed linear operator defined on the whole space is bounded.

The pentagram map is also defined on the larger space of twisted polygons.

The inverse cross ratio is used in order to define a coordinate system on the moduli space of polygons, both ordinary and twisted.

Same as Pure Nash Equilibrium, defined on the space of mixed strategies.

Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces.

In some sense, the two norms are "almost equivalent", even though they are not both defined on the same space.