Coherent topology information

topology, a coherent topology is a topology that is uniquely determined by a family of subspaces. Loosely speaking, a topological space is coherent with...

that the final topology often appears. A topology is coherent with some collection of subspaces if and only if it is the final topology induced by the...

X {\displaystyle X} is then compactly generated exactly when its topology is coherent with that family of subspaces; namely, a set A ⊆ X {\displaystyle...

commutative ring. It is sometimes also called a coherent space because of the connection to coherent topoi. Let X be a topological space and let K ∘ {\displaystyle...

manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The definition of coherent sheaves...

that all the inclusions are continuous (an example of a coherent topology). With this topology, K ∞ {\displaystyle \mathbb {K} ^{\infty }} becomes a complete...

{O}}_{X}} is not coherent, working with coherent sheaves has awkwardness (namely the kernel of a finite presentation can fail to be coherent). Because of...

'topology is rubber-sheet geometry'. Subfields of topology include geometric topology, differential topology, algebraic topology and general topology....

Zariski topology, and the second using the classical (Euclidean) topology.) For example, the equivalence between algebraic and analytic coherent sheaves...

In topology and related areas of mathematics, a Stone space, also known as a profinite space or profinite set, is a compact totally disconnected Hausdorff...

I{\text{ is an ideal of }}R\}.} This topology is called the Zariski topology. A basis for the Zariski topology can be constructed as follows. For f ∈...

show that the coherent topology induced by compact Hausdorff subspaces preserves the compact Hausdorff subspaces and their subspace topology requires that...

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré...

The Scalable Coherent Interface or Scalable Coherent Interconnect (SCI), is a high-speed interconnect standard for shared memory multiprocessing and message...

In physics, a squeezed coherent state is a quantum state that is usually described by two non-commuting observables having continuous spectra of eigenvalues...

functor. The prototypical theorem relating X and Xan says that for any two coherent sheaves F {\displaystyle {\mathcal {F}}} and G {\displaystyle {\mathcal...

category CohSp of coherent spaces (and coherent maps) is equivalent to the category CohLoc of coherent (or spectral) locales (and coherent maps), on the assumption...

In topology, an Alexandrov topology is a topology in which the intersection of every family of open sets is open. It is an axiom of topology that the...

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated...

low-latency coherent interconnect for scalable multiprocessor systems with a shared address space. It uses a directory-based home snoop coherency protocol...

Auroux (born April 1977) is a French mathematician working in geometry and topology. Auroux was admitted in 1993 to the École normale supérieure. In 1994,...

algebraic geometry, the Nisnevich topology, sometimes called the completely decomposed topology, is a Grothendieck topology on the category of schemes which...

Coherent states have been introduced in a physical context, first as quasi-classical states in quantum mechanics, then as the backbone of quantum optics...