Related papers: Zero and uniqueness sets for Fock spaces

If an automorphism f of a structure M is such that fix(f^k) = fix(f) for all positive k, then M|fix(f) is a substructure of M. The possible isomorphism types of such M|fix(f) are characterized when M is countable and arithmetically…

In this paper we consider the structure of the singularity sets associated with generalized functions in certain space-time foam algebras of generalized functions. In particular, we consider the algebra that is defined in terms of an…

We study the set of irregular points for topologically mixing subshifts of finite type. It is well known that despite the irregular set having zero measure for every invariant measure, it has full topological entropy and full Hausdorff…

A topological space is iso-dense if it has a dense set of isolated points. A topological space is scattered if each of its non-empty subspaces has an isolated point. In $\mathbf{ZF}$, in the absence of the axiom of choice, basic properties…

Let $A$ be a unital simple separable exact C$^*$-algebra which is approximately divisible and of real rank zero. We prove that the set of positive elements in $A$ with a fixed non-compact Cuntz class has vanishing homotopy groups. Combined…

In this paper, we introduce the Fock space over $\mathbb{C}^{\infty}$ and obtain an isomorphism between the Fock space over $\mathbb{C}^{\infty}$ and Bose-Fock space. Based on this isomorphism, we obtain representations of some operators on…

A major problem in the quantization of fields in curved spacetimes is the ambiguity in the choice of a Fock representation for the canonical commutation relations. There exists an infinite number of choices leading to different physical…

We prove that many completeness properties coincide in metric spaces, precompact groups and dense subgroups of products of separable metric groups. We apply these results to function spaces C_p(X,G) of G-valued continuous functions on a…

Let $X$ be a (real or complex) infinite dimensional linear space. We establish conditions on a homogeneous polynomial $P$ on $X$ so that, if $W$ is any finite dimensional subspace of $X$ on which $P$ vanishes, then $P$ vanishes on an…

We show that the following are consistent with ZFC: 1. Strongly meager sets form an ideal with the same additivity as the ideal of meager sets. 2. There exists a strong measure zero set of size > d (dominating number).

Consider a finite l-group acting on the affine space of dimension n over a field k, whose characteristic differs from l. We prove the existence of a fixed point, rational over k, in the following cases: --- The field k is p-special for some…

We study geometric and topological properties of locally compact, geodesically complete spaces with an upper curvature bound. We control the size of singular subsets, discuss homotopical and measure-theoretic stratifications and regularity…

Let E be a topological space and F a uniform space. We introduce a new topology (in fact a uniform structure) called the V-congergence on the space of applications from E to F such that C(E,F) is closed for this topology and the restriction…

We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.

The idea of monotonicity (or positive-definiteness in the linear case) is shown to be the central theme of the solution theories associated with problems of mathematical physics. A "grand unified" setting is surveyed covering a…

By studying the group of self homotopy equivalences of the localization (at a prime $p$ and/or zero) of some aspherical complexes, we show that, contrary to the case when the considered space is a nilpotent complex, $\mathcal{E}_{\#}^m…

If ZFC is consistent, then each of the following are consistent with ZFC + 2^{{aleph_0}}= aleph_2 : 1.) X subseteq R is of strong measure zero iff |X| <= aleph_1 + there is a generalized Sierpinski set. 2.) The union of aleph_1 many strong…

We show that if a closed discrete subset $A \subseteq \mathbf{R}^d$ is denser than a certain critical threshold, then $A$ is a Fourier uniqueness set, while if $A$ is sparser, then uniqueness fails and one can prescribe arbitrary values for…

In this paper we solve in the positive the question of whether any finite set of integers, containing the zero, is the mapping degree set between two oriented closed connected manifolds of the same dimension. We extend this question to the…

We study the set of chords of a real-valued continuous function on [0,1] with f(0)=f(1)=0. We describe which chords may appear as isolated points and provide examples illustrating our characterization. Maximal Hopf sets are introduced and…