Related papers: Comparing weak versions of separability
Many catalogues of isolated compact groups of galaxies (CGs) have been extracted using Hickson's criteria to identify isolated, dense systems of galaxies, with at least three or four galaxies concordant in magnitude and redshift. But is not…
We study point-separating function sets that are minimal with respect to the property of being separating. We first show that for a compact space $X$ having a minimal separating function set in $C_p(X)$ is equivalent to having a minimal…
The main goal of this work is to construct and study a reasonable compactification of the strata of the moduli space of Abelian differentials. This allows us to compute the Kodaira dimension of some strata of the moduli space of Abelian…
In this paper, we systematically develop the $m$-contiguity distance between simplicial maps as a discrete approximation framework for homotopical complexity in the category of simplicial complexes. We construct an increasing sequence of…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
In this paper, we deal with a hyperspace selection problem in the setting of connected spaces. We present two solutions of this problem illustrating the difference between selections for the nonempty closed sets, and those for the at most…
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When…
By using a selective filtration argument, we prove that the satisfiability problem of the unimodal logic of density is in $EXPTIME$. By using a tableau-like approach, we prove that the satisfiability problem of the bimodal logic of weak…
We study measurable spaces equipped with a $\sigma$-ideal of negligible sets. We find conditions under which they admit a localizable locally determined version -- a kind of fiber space that describes locally their directions -- defined by…
We use a method involving elementary submodels and a partial converse of Foran lemma to prove separable reduction theorems concerning Suslin sigma-P-porous sets where "P" can be from a rather wide class of porosity-like relations in…
In a series of papers with Kossakowski, the first author has examined properties of densities for which the positive partial transpositrionm (PPT) property can be readily checked. These densities were also investigated from a different…
The abscissas of convergence, uniform convergence and absolute convergence of vector valued Dirichlet series with respect to the original topology and with respect to the weak topology $\sigma(X,X')$ of a locally convex space $X$, in…
We give new examples of weak Hilbert spaces.
We aim to collect buried lemmas that are useful for proofs. In particular, we try to provide self-contained proofs for those lemmas and categorise them according to their usage.
We revisit the questions of density of smooth functions, and differential forms, in Sobolev spaces on Riemannian manifolds. We carefully show equivalence of weak covariant derivatives to weak partial derivatives.
the main goal of this paper is to prove that any Banach space X, that every dual ball in X** is weak* -separable, or every weak* -closed convex subset in X** is weak* -separable, or every norm-closed convex set in X* is constructible,…
We study properties of the weighted Bergman hernel on the unit disk. As we restrict to the subspace of all functions that vanish at a given point, we obtain the reproducing kernel for the subspace from the above weighted Bergman kernel via…
Context. The density split statistics in weak gravitational lensing analyses probes the correlation between regions of different (foreground) galaxy number densities and their weak lensing signal, measured by the shape distortion of…
After reviewing the interplay between frames and lower semi-frames, we introduce the notion of lower semi-frame controlled by a densely defined operator $A$ or, for short, a \emph{weak lower $A$-semi-frame} and we study its properties. In…
We show that the statement ``In every separable pseudometric space there is a maximal non-strictly \delta-separated set.'' implies the axiom of choice for countable families of sets. This gives answers to a question of Dybowski and…