Related papers: Comparing weak versions of separability
We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting objects are represented by stacks of measurable [0,1]-valued…
The density topology $\cal T$ is a topology on the real line, finer than the usual topology, having as its open sets the measurable subsets of ${\mathbb R}$, which are of density 1 at each of their points. The aim of this paper is to…
The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft…
In this paper we study the behaviour of selective separability properties in the class of Frech\'{e}t-Urysohn spaces. We present two examples, the first one given in ZFC proves the existence of a countable Frech\'{e}t-Urysohn (hence…
Previously, Wilson surface observables were interpreted as a class of Poisson sigma models. We profit from this construction to define and study the super version of Wilson surfaces. We provide some `proof of concept' examples to illustrate…
A standard introductory result is that Hausdorff spaces have the property US, that is, each convergent sequence has a unique limit. This paper explores several existing and new characterizations of separation axioms that are strictly weaker…
We investigate infinite versions of vector and affine space partition results, and thus obtain examples and a counterexample for a partition problem for relational structures. In particular we provide two (related) examples of an age…
Context. Weak lensing and clustering statistics beyond two-point functions can capture non-Gaussian information about the matter density field, thereby improving the constraints on cosmological parameters relative to the mainstream methods…
In Euclidean spaces, every closed, bounded, convex set can be characterized by two equivalent notions of separation properties. This is not true in general for arbitrary Banach spaces. In this work, we present a ball separation…
In this paper we explore relationships between divergence and thick groups, and with the same techniques we estimate lengths of shortest conjugators. We produce examples, for every positive integer n, of CAT(0) groups which are thick of…
This note identifies compact and {\sigma}-compact subsets of probability measures on a class of metric spaces with respect to the weak convergence topology. Moreover, it is shown by an example, that the space of probability measures on a…
The nature of compact groups (CGs) of galaxies, apparently so dense that the galaxies often overlap, is still a subject of debate: Are CGs roughly as dense in 3D as they appear in projection? Or are they caused by chance alignments of…
The paper first covers several properties of the extension of the divisibility relation to a set ${}^*\hspace{-0.5mm}N$ of nonstandard integers. After that, a connection is established with the divisibility in the Stone-\v{C}ech…
In this paper we present a brief study of the $\sigma$-set-$\sigma$-antiset duality that occurs in $\sigma$-set theory and we also present the development of the integer space $3^{A}=\left\langle 2^{A}, 2^{A^{-}} \right\rangle$ for the…
We investigate three combinatorial problems considered by Erd\"os, Rivat, Sark\"ozy and Sch\"on regarding divisibility properties of sum sets and sets of shifted products of integers in the context of function fields. Our results in this…
We randomly construct various subsets $\Lambda$ of the integers which have both smallness and largeness properties. They are small since they are very close, in various meanings, to Sidon sets: the continuous functions with spectrum in…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
This article fits in the context of the approach to topological problems in terms of the underlying convergence space structures, and serves as yet another illustration of the power of the method. More specifically, we spell out…
We provides some new equivalent forms of collection principle over some very weak set theories after reviewing the existing ones.
In the second section, we introduce dense unital magmas and show that a near-ring is dense if and only if it has a positive element smaller that unity. In the third section, we discuss magma-valued metric spaces. The density property of the…