 Minkowski space

${\mathbb{R}}^4$ with a weird dot product-like operation called the Minkowski inner product.

Because the Minkowski inner product product is not positive definite, the norm induced by an inner product is a norm, and the space is not a metric space strictly speaking.

The name given to this type of space is a pseudometric space.

Minkowski space is a mathematical structure that combines the three dimensions of space with the dimension of time into a four-dimensional manifold. It is a fundamental concept in the field of special relativity, formulated by the mathematician Hermann Minkowski in 1907. In Minkowski space, the geometry is governed by the Minkowski metric, which differs from the familiar Euclidean metric used in classical three-dimensional space.