相关论文: Sigma-continuity with closed witnesses
In this paper, we prove a result on non-Baire sets in category bases which when applied together with a result of Grzegorek yeilds a comparatively stronger version of a decomposition theorem due to Ulam.
Gravity theories are constructed on finite groups G. A self-consistent review of the differential calculi on finite G is given, with some new developments. The example of a bicovariant differential calculus on the nonabelian finite group…
We present $\sigma$-strongly functionally discrete mappings which expand the class of $\sigma$-discrete mappings and generalize Banach's theorem on analytically representable functions
The Blok-Esakia Theorem establishes that the lattice of superintuitionistic logics is isomorphic to the lattice of extensions of Grzegorczyk's logic. We prove that the Blok-Esakia isomorphism $\sigma$ does not extend to the fragments of the…
We extend the Brauer-Siegel theorem to new families of number fields, both in the classical setting of asymptotically bad families and in the more general framework due to Tsfasman and Vl\u{a}du\c{t} of asymptotically exact families. We…
In earlier works on Shape Dynamics (SD), a linear method of solving a particular set of Lichnerowicz-type equations through the implicit function theorem was developed in order to implicitly construct SD's global Hamiltonian and eliminate…
In this paper, we study the employment of $\Sigma_1$-sentences with certificates, i.e., $\Sigma_1$-sentences where a number of principles is added to ensure that the witness is sufficiently number-like. We develop certificates in some…
This article summarises the theory of several bounded functional calculi for unbounded operators that have recently been discovered. The extend the Hille--Phillips calculus for (negative) generators $A$ of certain bounded $C_0$-semigroups,…
We consider wave equations with a critically singular potential $\xi \cdot \sigma^{-2}$ diverging as an inverse square at a hypersurface $\sigma = 0$. Our aim is to construct counterexamples to unique continuation from $\sigma = 0$ for this…
We prove that for any $\alpha\in[0,\omega_1)$ there exists a strongly separately continuous function $f:\ell_\infty\to [0,1]$ such that $f$ belongs to the $(\alpha+1)$'th /$(\alpha+2)$'th/ Baire class and does not belong to the $\alpha$'th…
We establish the geometric Bogomolov conjecture for semiabelian varieties over function fields. We show a closed subvariety contains Zariski dense sets of small points, if and only if, after modulo its stabilizer, it is a torsion translate…
We discuss 2-dimmensional non-linear sigma-models on the Kaehler manifold G/H in the first order formalisim. Using the Berkovits method we explicitly construct the G-symmetry currents and primaries, when G/H are irreducible. It is a variant…
We show that Sobczyk's Theorem holds for a new class of Banach spaces, namely spaces of continuous functions on linearly ordered compacta.
Near every point of a real-analytic set in $\mathbb R^n$, we make use of Hironaka's resolution of singularity theorem to construct a family of continuous functions in $W^{1, 1}_{loc}$ such that their weak derivatives have (removable)…
We present a fixed point theorem for a class of (potentially) non-monotonic functions over specially structured complete lattices. The theorem has as a special case the Knaster-Tarski fixed point theorem when restricted to the case of…
In this paper, we refine the function $g(x)$ on Grimm's conjecture and improve a result of Erd\"{o}s and Selfridge without using Hall's theorem.
Groups $\Pi_k(X;\sigma)$ of "flagged homotopies" are introduced of which the usual (abelian for $k>1$) homotopy groups $\pi_k(X;p)$ is the limit case for flags $\sigma$ contracted to a point $p$. Calculus of exterior forms with values in…
We investigate extensions of S. Solecki's theorem on closing off finite partial isometries of metric spaces \cite{solecki1} and obtain the following exact equivalence: any action of a discrete group $\Gamma$ by isometries of a metric space…
A slalom is a sequence of finite sets of length omega. Slaloms are ordered by coordinatewise inclusion with finitely many exceptions. Improving earlier results of Mildenberger, Shelah and Tsaban, we prove consistency results concerning…
The separately continuity topology is considered and some its properties are investigated. With help of these properties a generalization of Sierpinski theorem on determination of real separately continuous function by its values on an…