Dimension theory

invariant

mathematical quantity

In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety of dimension , which is embedded in an ambient space of dimension , generally a Euclidean space, an affine space or a projective space. Hypersurfaces share, with surfaces in a three-dimensional space, the property of being defined by a single implicit equation, at least locally (near every point), and sometimes globally.

topological space that has small inductive dimension zero

invariant associated to a topological space; the smallest integer 𝑛 such that, for every cover, there is a refinement in which every point lies in the intersection of at most 𝑛+1 covering sets

fractal measurement

way of determining the dimension of a fractal set

In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties.

system with multiple fractal dimensions

topologically invariant definition of the dimension of a space