Related papers: On some recent selective properties involving netw…
The property of being selectively separable is well-studied and generalizations such as H-separable and wH-separable have also generated much interest. Bardyla, Maesano, and Zdomskyy proved from Martin's Axiom that there are countable…
This paper addresses several questions of Feng, Gruenhage, and Shen which arose from Michael's theory of continuous selections from countable spaces. We construct an example of a space which is $L$-selective but not $\mathbb{Q}$-selective…
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…
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…
In this paper we consider some recent relative versions of Menger property called set strongly star Menger and set star Menger properties and the corresponding Hurewicz-type properties. In particular, using \cite {BMae}, we "easily" prove…
A random null model termed the Blind Watchmaker network (BW) has been shown to reproduce the degree distribution found in metabolic networks. This might suggest that natural selection has had little influence on this particular network…
In this paper, we introduce the notions of Star-$\sigma\mathcal{K}$ and absolutely Star-$\sigma\mathcal{K}$ spaces which allow us to unify results among several properties in the theory of star selection principles on small spaces. In…
The aim of the paper is to highlight some open problems concerning approximation properties of Hardy spaces. We also present some results on the bounded compact and the dual compact approximation properties (shortly, BCAP and DCAP) of such…
In this article, we consider the following fractional {Hardy-type} inequality: \begin{align} \label{Fractional Hardy_abst} \int_{\mathbb{R}^N} |w(x)||u(x)|^p \mathrm{d}x \leq C \int_{\mathbb{R}^N \times \mathbb{R}^N}…
We initiate a study of varieties of minimal degree in weighted projective spaces. We call a weighted projective space $\mathbf{P}(w_0,\dots,w_n)$ divisible if $w_i \mid w_{i+1}$ for all $i$. We provide sharp bounds for when a non-degenerate…
We consider two-class linear classification in a high-dimensional, low-sample size setting. Only a small fraction of the features are useful, the useful features are unknown to us, and each useful feature contributes weakly to the…
In this paper we are interested in finding and evaluating cardinal characteristics of the continuum that appear in large-scale topology, usually as the smallest weights of coarse structures that belong to certain classes (indiscrete,…
The characters of irreducible finite dimensional representations of compact simple Lie group G are invariant with respect to the action of the Weyl group W(G) of G. The defining property of the new character-like functions ("hybrid…
For A a separable unital C*-algebra and M a separable McDuff II_1-factor, we show that the space Hom_w(A,M) of weak approximate unitary equivalence classes of unital *-homomorphisms A \rightarrow M may be considered as a closed, bounded,…
We characterize those generating functions k that produce weighted Hardy spaces of the unit disk D supporting nontrivial Hermitian weighted composition operators. Our characterization shows that the spaces associated with the "classical…
In this paper, we investigate properties of countable stationary towers. We derive the regularity properties of sets of reals in $L(\mathbf R)$ from some properties of countable stationary towers without explicit use of strong large…
Hart and Kunen, and independently in the recent preprint arXiv:2304.13113, R\'ios-Herrej\'on defined and studied the class $C({\omega}_1)$ of topological spaces $X$ having the property that for every neighborhood assignment $\{U(y) : y \in…
Projective Reed-Muller codes correspond to subcodes of the Reed-Muller code in which the polynomials being evaluated to yield codewords, are restricted to be homogeneous. The Generalized Hamming Weights (GHW) of a code ${\cal C}$, identify…
The paper deals with weighted spaces $L_p^w(G)$ on a locally compact group G. If w is a positive measurable function on G then we define the space $L_p^w(G)$, $p\ge1$, as $L_p^w(G)=\{f:fw\in L_p(G)\}$. We consider weights such that these…
Small-world networks, i.e. networks displaying both a high clustering coefficient and a small characteristic path length, are obliquitous in nature. Since their identification, the "small-worldness" metric, as proposed by Humphries and…