Holesabsence

Holesabsence is a term used to describe the absence of holes within a structure, space, or dataset. In formal discussions it denotes a condition where topological cavities of certain dimensions are absent, or where the space is topologically simple enough to have trivial homology up to a specified dimension.

Origin and usage: The term is not standardized; it appears informally in topology, materials science, and data analysis as a shorthand for topological simplicity.

Formal framing: In topology, holesabsence up to dimension d means that Hk(X) = 0 for all k with 0 < k ≤ d (and usually that the space is connected, so H0 is Z). In data analysis, holesabsence can be inferred from persistent homology when no long-lived features appear in the persistence diagram.

Examples: A solid cube or any convex, contractible solid has holesabsence in all dimensions. A torus does not, since it has a nontrivial H1 (a loop).

Applications: It serves as a descriptor of porosity in materials, a quality criterion for meshes in computer graphics, and a summary statistic in topological data analysis.

See also: simply connected, contractible, homology, persistent homology, porosity, topological data analysis.