The infinite dimensional version of the transversality theorem takes into account that the manifolds may be modeled in Banach spaces.

Informally, a n-simplex is the higher dimensional version of a triangle.

He develops their theory and finds, among other things, the higher dimensional version of Euler's formula.

Gallai was the first to prove the higher dimensional version of van der Waerden's theorem.

Later, four more dimensions were used to arrive at the twelve dimensional version, which involves extra gravitational forces; one of these corresponds to quintessence.

There are higher dimensional versions of this fact using n-cubes of spaces.

This equivalence is important for higher dimensional versions of groups.

The final product was a three dimensional version of other dimensions.

The basic kite fold is used to produce rosettes that are a 3 dimensional version of the 2D design.

The statement is essentially the same as the finite dimensional version.