Extendible

Extendible is an adjective describing something that can be extended, increased, or expanded beyond its current boundaries. In everyday use it refers to objects, processes, or plans that are capable of growth or adaptation without fundamental changes to their essential structure.

In mathematics and logic, "extendible" is used in several specialized senses. In set theory, an extendible cardinal is a large cardinal defined via elementary embeddings that can be extended to larger universes; such cardinals are stronger than supercompact cardinals and have implications for consistency strength. In other mathematical contexts, extendibility may refer to the possibility of extending a function, model, or structure to a larger domain, often under specified preservation conditions.

In topology and analysis, extension problems study when a function defined on a subset can be extended to the ambient space. A classical result is the Tietze extension theorem, which guarantees the extension of continuous real-valued functions from closed subsets of normal spaces to the entire space.

In computer science and software engineering, extendibility describes the design quality that allows adding new features without breaking existing behavior. Techniques to improve extendibility include modular architecture, clear interfaces, and adherence to the open/closed principle. Extendible systems commonly employ plugins, adapters, or service-oriented components to accommodate future requirements.