In mathematics, the gluing axiom is introduced to define what a sheaf F {\displaystyle {\mathcal {F}}} on a topological space X {\displaystyle X} must...

Axiom of extensionality Axiom of empty set Axiom of pairing Axiom of union Axiom of infinity Axiom schema of replacement Axiom of power set Axiom of...

because it is constant. It satisfies the gluing axiom, but is not a sheaf because it fails the local identity axiom on the empty set. This is because the...

a sheaf is a presheaf that satisfies the gluing axiom (here including the separation axiom). The gluing axiom is phrased in terms of pointwise covering...

a sheaf is supposed to be determined by its local restrictions (see gluing axiom), it can be expected that the stalks capture a fair amount of the information...

functions in bounded domains. Smoothness § Smooth partitions of unity Gluing axiom Fine sheaf Rudin, Walter (1987). Real and complex analysis (3rd ed.)...

possibility of restricting and of patching homeomorphisms (similar to the gluing axiom for sections of a sheaf). More precisely, a pseudogroup on a topological...

would go to show that κ+ ≤ κ, a contradiction. Esenin-Volpin's theorem Gluing axiom Neighbourhood system The empty set, which is always open, is the union...

whose existence is guaranteed by axiom 2 is called the gluing, concatenation, or collation of the sections si. By axiom 1 it is unique. Sections s i {\displaystyle...

Spec ⁡ ( R ) {\displaystyle \operatorname {Spec} (R)} and satisfies the gluing axiom. A sheaf of this form is called a quasicoherent sheaf. If P is a point...

category Localization of a category Enriched category Bicategory Sheaf Gluing axiom Descent (category theory) Grothendieck topology Introduction to topos...

the setup of almost ring theory. Analytic variety Catastrophe theory Gluing axiom Riemann surface Sheaf Stalk Tu, L. W. (2007). An introduction to manifolds...

that the representable functors are sheaves for it (i.e. a very general gluing axiom holds). Function field analogy It was realised in the nineteenth century...

{\mathsf {Sch}}_{S}} of S-schemes to the category of sets satisfying the gluing axiom; the perspective known as the functor of points. Under this perspective...

groups. One can show it is in fact a B-sheaf (i.e., it satisfies the gluing axiom) and thus defines the sheaf M ~ {\displaystyle {\widetilde {M}}} on X...

1] × [0,1] and gluing a pair of opposite edges on the boundary by a suitable diffeomorphism. A projective plane may be obtained by gluing a sphere with...

varieties, called schemes, by gluing together smaller pieces called affine schemes, similarly as manifolds can be built by gluing together open sets of Rn...

such gluing. The intuitive meaning of a stack is that it is a fibred category such that "all possible gluings work". The specification of gluings requires...

hereditarily quotient. Gluing. Topologists talk of gluing points together. If X {\displaystyle X} is a topological space, gluing the points x {\displaystyle...

eliminates all references to quantified elements from the axioms, and these algebraic laws may then be glued together in terms of a single functor F, the signature...

Atiyah's axioms are constructed by gluing the boundary with a differentiable (topological or continuous) transformation, while Segal's axioms are for conformal...

Aurora Beanstalk CloudFront DynamoDB EBS EC2 EFS ElastiCache EMR Glacier Glue Lambda Lightsail MTurk Neptune Product Advertising API RDS Redshift Rekognition...

taking the (single) edge of a Möbius strip and gluing it to itself in the correct direction, or by gluing the edge to a disk. Alternately, the real projective...

ideals of the spectrum. This allows gluing together algebraic varieties in a similar way as, for manifolds, charts are glued together for building a manifold...

algebraic varieties by gluing together affine varieties in a way similar to that in manifold theory, where manifolds are built by gluing together charts, which...

limit) is a construction that allows one to "glue together" several related objects, the precise gluing process being specified by morphisms between the...

\ldots ,\theta _{n}),\end{aligned}}} satisfying the following coherence axioms: identity: θ ∘ ( 1 , … , 1 ) = θ = 1 ∘ θ {\displaystyle \theta \circ (1...

thought of as a cut, then −a can be thought of as a gluing operation. Making a cut and then re-gluing it does not change the surface, so a + (−a) = 0. But...

relation. A ternary relation that satisfies the first three axioms, but not necessarily the axiom of totality, is a partial cyclic order. Given a linear order...

of the numbers 5, 6 or 7. The correct value may depend on the choice of axioms for set theory. The question can be phrased in graph theoretic terms as...