Related papers: On $\alpha$-embedded sets and extension of mapping…

We generalize Chirka's theorem on the extension of functions holomorphic in a neighbourhood of graph(F)\cup(\partial D\times D) -- where D is the open unit disc and graph(F) denotes the graph of a continuous D-valued function F -- to the…

We establish a cutting lemma for definable families of sets in distal structures, as well as the optimality of the distal cell decomposition for definable families of sets on the plane in $o$-minimal expansions of fields. Using it, we…

We investigate extension of a measure to a very general set of undetermined structure. Structure may be imposed on this set in special cases

We present some remarks about the embedding of spaces of Schwartz distributions into spaces of Colombeau generalized functions. We show that the various constructions of such embeddings existing in the literature lead in fact to the same…

We introduce the concept of linear topological modules over vertex algebras and apply it to representations of $\beta-\gamma$ system and affine Kac-Moody algebras.

We consider the problem of constructing a weakly-continuous mapping extending continuous mapping defined on a dense set of a topological space to the entire space. Theorem on necessary and sufficient conditions for the existence of such an…

We study the combinatorial and structural properties of the circle map sequences. We introduce an embedding procedure which gives a map from the hull(closure of the set of translates) to the sequence of embedding operations through which we…

We discuss the possibility of extending different versions of the Campbell-Magaard theorem, which have already been established in the context of semi-Riemannian geometry, to the context of Weyl's geometry. We show that some of the known…

As a generalization of Hausdorff's extension theorem of metrics, we prove an interpolation theorem of a family of metrics defined on closed subsets of metrizable spaces. As an application, we investigate typicality of subsets of moduli…

A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.

We generalize Barr's embedding theorem for regular categories to the context of enriched categories.

We use the theory of Harbater-Katz-Gabber curves to derive a generalization of the Hasse-Arf theorem for complete local field extensions in positive characteristic.

Let $\Omega$ be a perfectly normal topological space, let $A$ be a non-empty $G_\delta$-subset of $\Omega$ and let $B_1(A)$ denote the space of all functions $A\to\mathbb{R}$ of Baire-one class on $A$. Let also $\|\cdot\|_\infty$ be the…

We generalize Rado's extension theorem to complex spaces.

We consider a number of generalizations of the $\beta$-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations or derangements…

Let $\alpha,\beta \in \mathbb{R}_{>0}$ be such that $\alpha,\beta$ are quadratic and $\mathbb{Q}(\alpha)\neq \mathbb{Q}(\beta)$. Then every subset of $\mathbb{R}^n$ definable in both $(\mathbb{R},{<},+,\mathbb{Z},x\mapsto \alpha x)$ and…

The normal map given by Birkhoff orthogonality yields extensions of principal, Gaussian and mean curvatures to surfaces immersed in three-dimensional spaces whose geometry is given by an arbitrary norm and which are also called Minkowski…

We study embeddings between generalised Besov-Morrey spaces. Both sufficient and necessary conditions for the embeddings are proved. Embeddings of the Besov-Morrey spaces into the Lebesgue spaces are also considered. Our approach requires a…

The present article studies holomorphic isometric embeddings of arbitrary complex Grassmannians into quadrics, generalising results in [13]. The moduli spaces of these embeddings up to gauge and image equivalence are discussed using a…

We embed the geometries of the generalized $\lambda$-deformations into the framework of the Double Field Theory.