Related papers: An internal characterisation of radiality
The fundamental theories of physics are local theories, depending on local interactions of local variables. It is not clear if and how strictly local theories can produce non-local variables that have causal effectiveness. Yet, non-local…
We consider a crucial aspect of self-organization of a sensor network consisting of a large set of simple sensor nodes with no location hardware and only very limited communication range. After having been distributed randomly in a given…
We construct a family F of compact and pathwise connected subsets of the Euclidean plane such that (i) the cardinality of F is that of the continuum (and hence extremely large) and (ii) if X,Y are distinct spaces in F then there never…
We introduce soft bitopological spaces from the standpoint of soft elements. A soft bitopological space is a soft set equipped with two soft topologies. Following the classical construction of Goldar--Ray, each soft topology on $F$ induces…
We construct some new cohomology theories for topological groups and Lie groups and study some of its basic properties. For example, we introduce a cohomology theory based on measurable cochains which are continuous in a neighbourhood of…
We investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeomorphism. Geometrical properties of these curves such as…
We show that the first homology group of a locally connected compact metric space is either uncountable or is finitely generated. This is related to Shelah's well-known result which shows that the fundamental group of such a space satisfies…
A method for studying the causal structure of space-time evolution systems is presented. This method, based on a generalization of the well known Riemann problem, provides intrinsic results which can be interpreted from the geometrical…
We develop relativistic causality theory in the setting of point-free topology by introducing a notion of causal coverage in ordered locales, generalising their canonical coverage relation to incorporate causal structure. This improves…
We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…
Can we do a topological study of various classes of normal subgroups endowed with a hull-kernel-type topology? In this paper, we have provided an answer to this question. We have introduced as well a new class of normal subgroups called…
The recent characterization of transiting close-in planets has revealed an intriguing population of sub-Neptunes with highly tilted and even polar orbits relative to their host star's equator. Any viable theory for the origin of these…
A topological space $X$ is defined to have an $\omega^\omega$-base if at each point $x\in X$ the space $X$ has a neighborhood base $(U_\alpha[x])_{\alpha\in\omega^\omega}$ such that $U_\beta[x]\subset U_\alpha[x]$ for all $\alpha\le\beta$…
We study holomorphic $(n+1)$-chains $E_n\to E_{n-1} \to >... \to E_0$ consisting of holomorphic vector bundles over a compact Riemann surface and homomorphisms between them. A notion of stability depending on $n$ real parameters was…
The Kepler-discovered Systems with Tightly-packed Inner Planets (STIPs), typically with several planets of Earth to super-Earth masses on well-aligned, sub-AU orbits may host the most common type of planets, including habitable planets, in…
The method of the space dependent basis is applied to study electronic spinors in a crystal. The crystal in the momentum space is described by the Brillouine zone which might contains obstructions or degeneracies for which requires…
Quantum field theory predicts that dynamical curved spacetimes can spontaneously excite particle pairs from the quantum vacuum, a phenomenon extensively studied in expanding universes and in scenarios involving gravitational collapse. In…
Given an arbitrary spectral space $X$, we endow it with its specialization order $\leq$ and we study the interplay between suprema of subsets of $(X,\leq)$ and the constructible topology. More precisely, we investigate about when the…
Analysis on fractals is a growing field, with hints of potential for widespread applicability across all of STEM. One of the most heavily researched type of fractals are the nested fractals, fractal shapes defined by virtue of being made of…
Let $X$ be the prime spectrum of a ring. In [arXiv:0707.1525] the authors define a topology on $X$ by using ultrafilters and they show that this topology is precisely the constructible topology. In this paper we generalize the construction…