Related papers: Idealization of Ganster-Reilly decomposition theor…

A $P_\ell$-decomposition of a graph $G$ is a set of paths with $\ell$ edges in $G$ that cover the edge set of $G$. Favaron, Genest, and Kouider (2010) conjectured that every $(2k+1)$-regular graph that contains a perfect matching admits a…

We study the asymptotics at zero of continuous functions on (0, 1] by means of their asymptotic ideals, i.e., ideals in the ring of continuous functions on (0, 1] satisfying a polynomial growth condition at 0 modulo rapidly decreasing…

Consider a Henselian rank one valued field $K$ of equicharacteristic zero along with the language $\mathcal{L}^{P}$ of Denef--Pas. Let $f: A \to K$ be an $\mathcal{L}^{P}$-definable (with parameters) function on a subset $A$ of $K^{n}$. We…

It is proved that for every stratifiable space $Y$ and a closed subset $X\subset Y$ there exists a regular (i.e. linear positive with unit norm) extension operator $T:C(X\times X)\to C(Y\times Y)$ preserving the class of (pseudo)metrics.…

Let $D$ be a convex subset of a real vector space. It is shown that a radially lower semicontinuous function $f: D\to \mathbf{R}\cup \{+\infty\}$ is convex if and only if for all $x,y \in D$ there exists $\alpha=\alpha(x,y) \in (0,1)$ such…

The generalized test ideals introduced in [HY] are related to multiplier ideals via reduction to characteristic p. In addition, they satisfy many of the subtle properties of the multiplier ideals, which in characteristic zero follow via…

It is investigated the existence of a separately continuous function $f:X\times Y\to \mathbb R$ with an onepoint set of discontinuity for topological spaces $X$ and $Y$ which satisfy compactness type conditions. In particular, it is shown…

Let X be a countably infinite set of real numbers and let Y_x, x \in X, be an independent family of stationary random subsets of the real numbers, e.g. homogeneous Poisson point processes. We give criteria for the a.s. existence of various…

A $\sigma$-ideal $\cal{I}$ on a set $X$ is supersaturated if for every family $\cal{F}$ of $\cal{I}$-positive sets with $|\cal{F}| < \mathrm{add}(\cal{I})$, there exists a countable set that meets every set in $\cal{F}$. We show that many…

We give necessary and sufficient conditions for a function in a naturally appearing functional space to be a fixed point of the Ruelle-Thurston operator associated to a rational function, see Lemma 2.1. The proof uses essentially a recent…

For a family of continuous functions $f_1,f_2,\dots \colon I \to \mathbb{R}$ ($I$ is a fixed interval) with $f_1\le f_2\le \dots$ define a set $$ I_f:=\big\{x \in I \colon \lim_{n \to \infty} f_n(x)=+\infty\big\}.$$ We study the properties…

Let $(X, \mathscr{L}, \lambda)$ and $(Y, \mathscr{M}, \mu)$ be finite measure spaces for which there exist $A \in \mathscr{L}$ and $B \in \mathscr{M}$ with $0 < \lambda(A) < \lambda(X)$ and $0 < \mu(B) < \mu(Y)$, and let $I\subseteq…

Let $X$ be a first countable Hausdorff topological group. The limit of a sequence in $X$ defines a function denoted by $lim$ from the set of all convergence sequences to $X$. This definition was modified by Connor and Grosse-Erdmann for…

For a measurable space ($X,\mathcal{A}$), let $\mathcal{M}(X,\mathcal{A})$ be the corresponding ring of all real valued measurable functions and let $\mu$ be a measure on ($X,\mathcal{A}$). In this paper, we generalize the so-called…

Using a generalization of forward elimination, it is proved that functions $f_1,...,f_n:X\to\mathbb{A}$, where $\mathbb{A}$ is a field, are linearly independent if and only if there exists a nonsingular matrix $[f_i(x_j)]$ of size $n$,…

This part of a multi-paper project studies the lattice properties of the arithmetic mean ideals of B(H) introduced by Dykema, Figiel, Weiss, and Wodzicki. We prove: the lattices of all principal ideals, of arithmetic mean or arithmetic mean…

Ideals in infinite-dimensional polynomial rings that are invariant under the action of the monoid of increasing functions have been extensively studied recently. Of particular interest is the asymptotic behavior of truncations of such an…

We prove that a real x is 1-generic if and only if every differentiable computable function has continuous derivative at x. This provides a counterpart to recent results connecting effective notions of randomness with differentiability. We…

Inspired by recent work of A. Mardani which elaborates on the elementary fact that for any continuous function $f:\omega_1\times\mathbb{R}\to\mathbb{R}$, there is an $\alpha\in\omega_1$ such that $f(\langle\beta,x\rangle) =…

We establish a Fenchel-Moreau type theorem for proper convex functions $f\colon X\to \bar{L}^0$, where $(X, Y, \langle \cdot,\cdot \rangle)$ is a dual pair of Banach spaces and $\bar L^0$ is the space of all extended real-valued functions…