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An area-preserving affine transformation. Equiaffinities include the crossed hyperbolic rotation, elliptic rotation, hyperbolic rotation, and parabolic rotation.

A geometry constructed without reference to measurement. The only primitive concepts are those of points and intermediacy. There are 10 axioms underlying ordered geometry.

Transitivity is a result of the symmetry in the group. A group G is called transitive if its group action (understood to be a subgroup of a permutation group on a set Omega) ...

Codimension is a term used in a number of algebraic and geometric contexts to indicate the difference between the dimension of certain objects and the dimension of a smaller ...

The differential forms on C^n decompose into forms of type (p,q), sometimes called (p,q)-forms. For example, on C, the exterior algebra decomposes into four types: ^ C = ^ ^0 ...

If g is a Lie algebra, then a subspace a of g is said to be a Lie subalgebra if it is closed under the Lie bracket. That is, a is a Lie subalgebra of g if for all x,y in a, ...

A Banach space X is called minimal if every infinite-dimensional subspace Y of X contains a subspace Z isomorphic to X. An example of a minimal Banach space is the Banach ...

If y has period 2pi, y^' is L^2, and int_0^(2pi)ydx=0, (1) then int_0^(2pi)y^2dx<int_0^(2pi)y^('2)dx (2) unless y=Acosx+Bsinx (3) (Hardy et al. 1988). Another inequality ...

For a finite group G, let p(G) be the subgroup generated by all the Sylow p-subgroups of G. If X is a projective curve in characteristic p>0, and if x_0, ..., x_t are points ...

A homeomorphism, also called a continuous transformation, is an equivalence relation and one-to-one correspondence between points in two geometric figures or topological ...