Higher dimension

From Wikipedia, the free encyclopedia

Higher dimension as a term in mathematics most commonly refers to any number of spatial dimensions greater than three.

The three standard dimensions are length, width, and breadth (or height). The first higher dimension required is often time, and space-time is the most common example of a four-dimensional space.

It is commonplace in advanced pure and applied mathematics to study abstract sets and applied models with many dimensions. Fairly simple constructions yield spaces with arbitrarily high positive integer dimension, and only slightly more sophistication is required to construct spaces of infinite dimension.

In geometric topology, the nature of the difficulties in the subject has turned out to be such that dimensions 3 and 4 are the most resistant (see for example Whitney disc). Therefore in that context higher dimension usually means dimension ≥ 5.