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In mathematics, noncommutative topology is a term used for the relationship between topological and C*-algebraic concepts. The term has its origins in...

e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions. An approach giving deep insight about noncommutative spaces...

non-commutative algebraic objects. Noncommutative geometry Noncommutative harmonic analysis see representation theory Noncommutative topology Nonlinear analysis Nonlinear...

can recover the topology of the space from the algebraic properties of its algebra of continuous functions. This leads to noncommutative geometry, where...

algebras has been called noncommutative measure theory, while the theory of C*-algebras is sometimes called noncommutative topology (Connes 1994). Operators...

its spectrum. Generalizing to non-commutative C*-algebras yields noncommutative topology. Scheme (mathematics) Projective scheme Spectrum of a matrix Serre's...

mathematics, nonabelian algebraic topology studies an aspect of algebraic topology that involves (inevitably noncommutative) higher-dimensional algebras....

This characterization is one of the motivations for the noncommutative topology and noncommutative geometry programs. Given a Banach *-algebra A with an...

development of the Baum–Connes conjecture and plays a crucial role in noncommutative topology. KK-theory was followed by a series of similar bifunctor constructions...

equivalent to noncommutative rings, so Morita equivalence is coarser than isomorphism. Morita equivalence is especially important in algebraic topology and functional...

Spinors and Twistors Applications to: Strings and Superstrings Noncommutative Topology and Geometry Quantum Groups Geometric Methods in Statistics and...

In mathematics, noncommutative harmonic analysis is the field in which results from Fourier analysis are extended to topological groups that are not commutative...

recent focus on noncommutative geometry appears to be very much in line with the work of Fred van Oystaeyen on noncommutative topology. Ignazio Licata...

the philosophy of noncommutative geometry, which tries to study various non-classical and/or pathological objects by noncommutative operator algebras...

(knot theory) Listing number Mereotopology Noncommutative topology Pointless topology Set-theoretic topology Topological combinatorics Topological data...

(equivalently: associative and commutative) isomorphic to the quaternions if noncommutative but associative isomorphic to the octonions if non-associative but alternative...

Model (best known as Spectral Standard Model ), is a model based on noncommutative geometry that unifies a modified form of general relativity with the...

One of his recent books, Virtual Topology and Functor Geometry, provides an introduction to noncommutative topology. At the occasion of his 60th birthday...

The study of rings that are not necessarily commutative is known as noncommutative algebra; it includes ring theory, representation theory, and the theory...

Homotopical algebra; Topology using categories, including algebraic topology, categorical topology, quantum topology, low-dimensional topology; Categorical logic...