Related papers: On $\alpha$-embedded sets and extension of mapping…
In this paper, we have obtained a generalization of the Grothendieck's theorem for the space of continuous mappings $C_{\lambda,\mu}(X,Y)$ where $Y$ is a complete uniform space with the uniformity $\mu$ endowed with the topology of uniform…
Working in the framework of Borel reducibility, we study various notions of embeddability between groups. We prove that the embeddability between countable groups, the topological embeddability between (discrete) Polish groups, and the…
We relate extensions of completely unitary VOAs and (commutative) Q-systems. As an application, we show that any unitary extension of a completely unitary VOA is completely unitary.
In the Normed space theory, the existence of fixed points is one of the main tools in improving efficiency of iterative algorithms in optimization, numerical analysis and various mathematical applications. This study introduces and…
This paper introduces the Higman-Neumann-Neumann extension (HNN extension; for short) for Nijenhuis Lie algebras and provides an embedding theorem. To this end, we employ the theory of Gr\"obner-Shirshov basis for Lie {\Omega}-algebras in…
In this short paper, Kuratowski problem will be investigated in vector space. The highest number of distinct sets that can be generated from one convex set in linear space by repeatedly applying algebraic closure and complement in any order…
We extend logical categories with fiberwise interior and closure operators so as to obtain an embedding theorem into powers of the category of topological spaces. The required axioms, besides the Kuratowski closure axioms, are a `product…
A model with a sequence of indiscernibles depending on a particular precovering set is constructed.The initial assumption is as follows: for every n<omega the set {alpha | o(alpha)=alpha^+n } is unbounded in kappa.
We develop a theory of umkehr maps for twisted generalized homology theories. In this theory, interesting umkehr maps, including generalizations of important classical ones, are induced by cartesian morphisms of a certain category opfibred…
Basing ourselves on Janelidze and Kelly's general notion of central extension, we study universal central extensions in the context of semi-abelian categories. Thus we unify classical, recent and new results in one conceptual framework. The…
We consider Campanato spaces with exponents $\lambda , p$ on domains of class $C^{0,\gamma}$ in the N-dimensional Euclidean space endowed with a natural anisotropic metric depending on $\gamma$. We discuss several results including the…
In the article a technique of the usage of $f$-continuous functions (on mappings) and their families is developed. A proof of the Urysohn's Lemma for mappings is presented and a variant of the Brouwer-Tietze-Urysohn Extension Theorem for…
This paper is a contribution to the study of extensions of arbitrary models of ZF (Zermelo-Fraenkel set theory), with no regard to countability or well-foundedness of the models involved. We present some new constructions of certain types…
We study completely positive module maps on $C^{*}$-algebras which are $C^*$-module over another $C^*$-algebra with compatible actions. We extend several well known dilation and extension results to this setup, including the Stinespring…
Given a compact of ${\bf R}^n$, there is always a doubling measure having it as its support. We use this fact to construct an integral operator that extends differentiable functions defined on any compact set of ${\bf R}^n$ to the whole of…
We prove two extension theorems for positive maps from operator systems into matrix algebras
We study $\alpha$-adic expansions of numbers in an extension field, that is to say, left infinite representations of numbers in the positional numeration system with the base $\alpha$, where $\alpha$ is an algebraic conjugate of a Pisot…
In this paper, we introduce the notion of a topological groupoid extension and relate it to the already existing notion of a gerbe over a topological stack. We further study the properties of a gerbe over a Serre, Hurewicz stack.
The complementarity between signaling and randomness in any communicated resource that can simulate singlet statistics is generalized by relaxing the assumption of free will in the choice of measurement settings. We show how to construct an…
In this paper, we establish a theorem on extension of Lipschitz maps $f$ definable in Hensel minimal fields $K$. This may be regarded as a definable, non-Archimedean, non-locally compact version of Kirszbraun's extension theorem. We proceed…