extents

Extents is a term used in several disciplines to denote reach, range, or allocated space. In general topology, the extent of a topological space X is the supremum of the cardinalities of its closed discrete subspaces. This invariant measures how large closed discrete subsets can be, and it is studied alongside density, weight, and other size characteristics of spaces. In specific contexts, such as compact or separable spaces, the extent interacts with these invariants in ways that illuminate the structure of X.

In geometry and real analysis, the extent of a bounded subset of the real line is the distance between its endpoints: if A has a minimum and a maximum, ext(A) = max A − min A. In higher dimensions, the term is less standard, but the underlying idea of measuring how spread out a set is along coordinates remains common in describing a set’s range or spread.

In geography and geographic information systems, geographic extent (or bounding extent) describes the minimal axis-aligned rectangle that contains a geographic dataset, defined by its minimum and maximum coordinates. It serves as a quick descriptor of location and as a computational constraint for spatial operations.

In computing and storage, an extent is a contiguous region of storage allocated to a file or to a database object. Using extents reduces fragmentation and speeds sequential access. File systems such as NTFS and database systems like Oracle employ extent-based allocation to manage space efficiently.

Other common uses include referring to the extent of a territory or the general scope of a project or phenomenon.