Related papers: Uniform Interpolation and Compact Congruences
We study the symmetry properties of autonomous integrating factors from an algebraic point of view. The symmetries are delineated for the resulting integrals treated as equations and symmetries of the integrals treated as functions or…
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
The main aim of this paper to show how commutative algebra is connected to topology. We give underlying topological idea of some results on completable unimodular rows.
We introduce a notion of a uniform structure on the set of all representations of a given separable, not necessarilly commutative $C^*$-algebra $\mathfrak{A}$ by introducing a suitable family of metrics on the set of representations of…
In this short note we give a proof of the refined version of the uniform invariant approximation property for compact (non-commutative) groups following the Bourgain's approach.
In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…
In this article, we prove the following interpolation problem: if the composition of a function and a regular map between affine varieties is a regular function, then there exists a global regular function of the target variety that…
We discuss the existence of complete accumulation points of sequences in products of topological spaces. Then we collect and generalize many of the results proved in Parts I, II and IV. The present Part VI is complementary to Part V to the…
We prove an abstract theorem on keeping the compactness property of a linear operator after interpolation in Banach spaces. No analytical presentation of operators, spaces and interpolation functor is required. We use only some little-known…
A necessary and sufficient condition is provided for the solvability of a binomial congruence with a composite modulus, circumventing its prime factorization. This is a generalization of Euler's Criterion through that of Euler's Theorem,…
It is shown that the coloured isomorphism class of a unital, simple, $\mathcal{Z}$-stable, separable amenable C$^*$-algebra satisfying the Universal Coefficient Theorem (UCT) is determined by its tracial simplex.
The congruence subgroup property is established for the modular representations associated to any modular tensor category. This result is used to prove that the kernel of the representation of the modular group on the conformal blocks of…
We show that pseudovarieties of finitely generated algebras, i.e., classes $C$ of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can be described via a uniform structure $U$ on the free…
We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities of families. The most general form of this compactness notion depends on two ordinal parameters. In the…
We define a notion of general uniform interpolant, generalizing the notions of cover and of uniform interpolant and identify situations in which symbol elimination can be used for computing general uniform interpolants. We investigate the…
We show that for a complete complex algebraic variety the pure component of homology coincides with the image of intersection homology. Therefore pure homology is topologically invariant. To obtain slightly more general results we introduce…
It is shown that a large class of properties coincide for weighted composition operators on a large class of weighted VMOA spaces, including the ones with logarithmic weights and the ones with standard weights $(1-|z|)^{-c}, \ 0\leq c<…
Reflection principles (or dually speaking, compactness principles) often give rise to combinatorial guessing principles. Uniformization properties, on the other hand, are examples of anti-guessing principles. We discuss the tension and the…
Under what circumstances might every extension of a combinatorial structure contain more copies of another one than the original did? This property, which we call prolificity, holds universally in some cases (e.g., finite linear orders) and…