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...ts]] in highly abstract spaces. A set equipped with a metric is called a [[metric space]]. Let <math>X</math> be a given nonempty set. A metric on <math>X</math> is a function ...

...set|closed]] and [[Boundedness|bounded]]". In [[Euclidean space|Euclidean spaces]] <math>\mathbb{R}^n</math>, by the [[Heine–Borel theorem]], a set is compa ...eing closed and bounded, while still making sense in arbitrary topological spaces and preserving the essential properties of compact sets. ...

|property=Subspaces of Hausdorff spaces are Hausdorff. |property=Finite products of Hausdorff spaces are Hausdorff. ...

...idea of "nearness" without necessarily defining a [[metric]]. Topological spaces are the objects of study in [[general topology]]. Some key properties of topological spaces include: ...

...matical work. Computation is used to test conjectures, search large finite spaces, generate data, visualize structure, verify exceptional cases, and check fo ...minimum number of moves sufficient to solve any position in the half-turn metric. In 2010, Tomas Rokicki, Herbert Kociemba, Morley Davidson, and John Dethri ...