Noncommutative topology

Noncommutative topology in mathematics is a term applied to the strictly C*-algebraic part of the noncommutative geometry program. The program has its origins in the Gel'fand duality between the topology of locally compact spaces and the algebraic structure of commutative C*-algebras.

Related Topics:
Mathematics - C*-algebra - Noncommutative geometry - Gel'fand duality - Topology - Locally compact - Algebraic structure - Commutative

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Several topological properties can be formulated as properties for the C*-algebras without making reference to commutativity or the underlying space, and so have an immediate generalization.

Related Topics:
Topological - C*-algebras - Commutativity - Space

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Amongst these are compactness (being unital), dimension (real or stable rank), connectedness (projectionless algebra) and K-theory.

Related Topics:
Compactness - Unital - Dimension - Real - Stable rank - Connectedness - Projectionless algebra - K-theory

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