Related papers: Properties D and aD are different

We discuss various aspects of "braid spaces'' or configuration spaces of unordered points on manifolds. First we describe how the homology of these spaces is affected by puncturing the underlying manifold, hence extending some results of…

Equipped with the L^2-distortion distance, the space "X" of all metric measure spaces (X,d,m) is proven to have nonnegative curvature in the sense of Alexandrov. Geodesics and tangent spaces are characterized in detail. Moreover, classes of…

We show that there are locally compact spaces that can be condensed onto separable spaces but not onto compact separable spaces. We also show that for every cardinal $\kappa$ there is a locally compact topological group of cardinality…

The role of double space is essential in new interpretation of T-duality and consequently in an attempt to construct M-theory. The case of open string is missing in such approach because until now there have been no appropriate formulation…

We present a characterization of Valdivia compact spaces of small weight in terms of path spaces of trees and we use it to obtain (under $\diamondsuit$) a counterexample to a conjecture related to an open problem concerning twisted sums of…

An algebraic variety $X$ is called a homogeneous space if there exists a transitive regular action of an algebraic group on $X$. We prove inequalities between the dimension of a homogeneous space of a linear algebraic group and its Picard…

We show that the analogues of the Hamkins embedding theorems, proved for the countable models of set theory, do not hold when extended to the uncountable realm of $\omega_1$-like models of set theory. Specifically, under the $\diamondsuit$…

I argue that consistent geometrical descriptions of the universe are far from unique even as low-energy limits and that an abstract "atomic" description of spacetime and gauge-theoretic geometry in terms of K-theories of algebraic and…

We prove several results of the following type: given finite dimensional normed space V possessing certain geometric property there exists another space X having the same property and such that (1) log (dim X) = O(log (dim V)) and (2) every…

We consider codimension-one defects in the theory of $d$ compact scalars on a two-dimensional worldsheet, acting linearly by mixing the scalars and their duals. By requiring that the defects are topological, we find that they correspond to…

Dimensional types of metric scattered spaces are investigated. Revised proofs of Mazurkiewicz-Sierpi\'nski and Knaster-Urbanik theorems are presented. Embeddable properties of countable metric spaces are generalized onto uncountable metric…

The aim of this paper is to introduce a new class of softly normal called softly $\pi g\widehat{D}$ -normality by using $\pi g\widehat{D}$ -open sets and obtained several properties of such a space. We discuss many properties of this new…

We give a short proof of the fact that there are no measurable subsets of Euclidean space (in dimension d > 2), which, no matter how translated and rotated, always contain exactly one integer lattice point. In dimension d=2 (the original…

In this paper, we investigate a proper CAT(0) space $(X,d)$ which is homeomorphic to $R^2$ and we show that the asymptotic dimension $asdim (X,d)$ is equal to 2.

We give Ramsey expansions of classes of generalised metric spaces where distances come from a linearly ordered commutative monoid. This complements results of Conant about the extension property for partial automorphisms and extends an…

We survey explicit coordinate descriptions for two (A and X) versions of Teichmuller and lamination spaces for open 2D surfaces, and extend them to the more general set-up of surfaces with distinguished collections of points on the…

An $O(d,d)$ symmetry of the manifold of string vacua that do not depend on $d$ (out of $D$) space-time coordinates has been recently identified. Here we write down, for $d=D-1$, the low energy equations of motion and their general solution…

In this paper, we deal with uniform spaces whose diagonal uniformity admits a basis consisting of equivalence relations. Such non-Archimedean uniform spaces are particularly interesting for applications in commutative ring theory, because…

We consider constraints on $D$-dimensional theories in $M_D$, $dS_D$ and $AdS_D$ backgrounds in the light of AdS swampland conjectures as applied to their compactification in a circle. In particular we consider the non-SUSY AdS instability…

We characterize the finite dimensional asymmetric normed spaces which are right bounded and the relation of this property with the natural compactness properties of the unit ball, as compactness and strong compactness. In contrast with some…