Related papers: One Dimensional Locally Connected S-spaces

For a Tychonoff space $X$ and a family $\lambda$ of subsets of $X$, we denote by $C_{\lambda}(X)$ the space of all real-valued continuous functions on $X$ with the set-open topology. In this paper, we study the Menger and projective Menger…

Given a conserved and traceless energy-momentum tensor and a conformal Killing vector, one obtains a conserved current. We generalise this construction to superconformal theories in three, four, five and six dimensions with various amounts…

The following generalizations of the Chacon map are proposed: instead of classical constant spacer sequence $(0,1,0)$ let a sequence $(0,s_j,0)$ be one with unbounded $s_j$. (We mention also an analogue of the historical Chacon map with…

We consider the problem of digitalizing Euclidean segments. Specifically, we look for a constructive method to connect any two points in $\mathbb{Z}^d$. The construction must be {\em consistent} (that is, satisfy the natural extension of…

A curious correspondence has been known between Landau models and non-linear sigma models: Reinterpreting the base-manifolds of Landau models as field-manifolds, the Landau models are transformed to non-linear sigma models with same global…

In this correspondence, first-tier indirect (direct) discernible constellation expansions are defined for generalized orthogonal designs. The expanded signal constellation, leading to so-called super-orthogonal codes, allows the achievement…

We extend the result in J. Reine Angew. Math. 664, 29-53, to the non-compact case. Namely, we prove that the canonical connection on a simply connected and irreducible naturally reductive space is unique, provided the space is not a sphere,…

Strongly convex sets in Hilbert spaces are characterized by local properties. One quantity which is used for this purpose is a generalization of the modulus of convexity \delta_\Omega of a set \Omega. We also show that \lim_{\epsilon \to 0}…

The aim of this note is to prove that any compact metric space can be made connected at a minimal cost, where the cost is taken to be the one-dimensional Hausdorff measure.

In this article, we discuss fixed point results for $(\varepsilon,\lambda)$-uniformly locally contractive self mapping defined on $\varepsilon$-chainable $G$-metric type spaces. In particular, we show that under some more general…

We formalize the notion of limit of an inverse system of metric spaces with $1$-Lipschitz projections having unbounded fibers. The purpose is to use sub-Riemannian groups for metrizing the space of signatures of rectifiable paths in…

Let X be a connected open set in n-dimensional Euclidean space, partially ordered by a closed convex cone K with nonempty interior: y > x if and only if y-x is nonzero and in K. Theorem: If F is a monotone local flow in X whose periodic…

The hyperbolic spin chain is used to elucidate the notion of spontaneous symmetry breaking for a non-amenable internal symmetry group, here SO(1,2). The noncompact symmetry is shown to be spontaneously broken -- something which would be…

We introduce a new algebraic structure for multi-dimensional compositional embeddings, built on directional non-commutative monoidal operators. The core contribution of this work is this novel framework, which exhibits appealing theoretical…

This paper concerns the local connectedness of components of self-similar sets. Given an equal partition of the unit square into n*n small squares, we may choose arbitrarily two or more of them and form an iterated function system. The…

Considering that a position measurement can effectively involve a momentum-dependent shift and rescaling of the "true" space-time coordinates, we construct a set of effective space-time coordinates which are naturally non-commutative. They…

The Johnson-Lindenstrauss Lemma (J-L Lemma) is a cornerstone of dimension reduction techniques. We study it in the one-bit context, namely we consider the unit sphere $ \mathbb S ^{N-1}$, with normalized geodesic metric, and map a finite…

Let $(M, \omega)$ be a connected, compact 6-dimensional symplectic manifold equipped with a semi-free Hamiltonian $S^1$ action such that the fixed point set consists of isolated points or surfaces. Assume dim $H^2(M)<3$, in \cite{L}, we…

A locally convex space (lcs) $E$ is said to have an $\omega^{\omega}$-base if $E$ has a neighborhood base $\{U_{\alpha}:\alpha\in\omega^\omega\}$ at zero such that $U_{\beta}\subseteq U_{\alpha}$ for all $\alpha\leq\beta$. The class of lcs…

All spaces are assumed to be separable and metrizable. Ostrovsky showed that every zero-dimensional Borel space is $\sigma$-homogeneous. Inspired by this theorem, we obtain the following results: assuming $\mathsf{AD}$, every…