resolvable

Resolvable is an adjective meaning capable of being resolved, settled, or disentangled. In scholarly usage, the term signals that a given object admits a particular kind of resolution, decomposition, or partition into simpler components.

In topology and set theory, resolvability is a property of a topological space. A space is resolvable if it contains two disjoint dense subsets. This condition is weaker than separability and interacts with notions of density and cardinal invariants. The concept is mainly of interest in general topology and its set-theoretic relatives.

In algebraic geometry and singularity theory, a variety or space is often described as resolvable when it admits a resolution of singularities. A resolution is a process that replaces a space with a smoother one via a controlled birational transformation, so that the smooth model preserves essential geometric information. When such a resolution exists, the original space is said to be resolvable in this sense.

In group theory and Galois theory, the term resolvable has historical use as a synonym for solvable, indicating that a problem can be solved by a sequence of abelian or cyclic steps (for example, a polynomial being solvable by radicals). Today, the standard term is solvable, though some older literature or particular authors may still use resolvable with the same basic meaning.

In combinatorics, a resolvable design (such as a resolvable block design) is a combinatorial design whose blocks can be partitioned into parallel classes that cover each point exactly once per class. This property is important in experimental design and scheduling.

See also solvable, resolution, resolvent, resolvability.