kontinuitet

Kontinuitet describes the state of being continuous, without breaks or abrupt transitions, and is used across disciplines to denote connectedness in space, time, or form. The term stems from Latin continuus and appears in several languages with similar spellings, including Swedish, Norwegian, Danish, and Finnish.

In mathematics, continuity refers to a relation between a function and its input: small changes in the input produce small changes in the output. The standard definition uses limits or the epsilon–delta formulation: f is continuous at a point a if for every epsilon > 0 there exists delta > 0 such that |x − a| < delta implies |f(x) − f(a)| < epsilon. On a domain, continuity means the property holds at every point; continuous functions do not have jumps.

In topology, continuity is defined via the preimage of open sets: a map between topological spaces is continuous if the preimage of every open set is open. This abstraction underpins convergence and compactness and is central to analysis and geometry. In physics, continuity equations describe how quantities like mass or charge diffuse or flow, formalizing local conservation laws.

In philosophy and cognitive science, temporal continuity concerns how objects persist through time and how identity is maintained amid change. The concept also informs discussions about memory, succession, and events that seem to come in a seamless sequence.

In cultural and historical contexts, continuitet refers to the persistence of traditions, languages, institutions, or social practices across generations, often in balance with innovation and change.