Unterdimension

Unterdimension (literally "lower dimension") is a German term used to describe a dimension that is lower than a defined reference dimension. Its exact meaning is context-dependent, and there is no single formal definition attached to the term.

In mathematics, a subset of an n-dimensional space can have dimension strictly less than n, such as a line in the plane or a surface in space. In fractal geometry, the Hausdorff or box-counting dimension may be non-integer and fall below the ambient dimension. The term is often used informally for such cases.

In physics, the idea of an effective lower dimension appears in dimensional reduction, where higher-dimensional theories yield lower-dimensional behavior at specific scales, and in condensed matter systems with quasi-one- or quasi-two-dimensional dynamics.

In science fiction and popular writing, Unterdimension may denote a space or realm with reduced dimensionality, used as a plot device or metaphor.

Because it is not a fixed formal term, usage varies by author. In formal mathematics, more precise terms include submanifolds, lower-dimensional embeddings, or specific notions of fractal dimension.