Related papers: A semifilter approach to selection principles
It is consistent (relative to ZFC) that the union of max{b,g} many families in the Baire space which are not finitely dominating is not dominating. In particular, it is consistent that for each nonprincipal ultrafilter U, the cofinality of…
We examine dynamical systems with the property that pseudo-orbits can be traced by small diameter sets with bounded cardinality. In particular, we show that mixing sofic subshifts and surjective dynamical systems with the specification…
The theorem we prove is a slight strengthening of some results by Just, Miller, Scheepers and Szeptycki [JMSS]. We use the Michael technique instead of the combinatorial approach in the literature. Comments by the submitter: This short…
The main result is the following. Let $f \colon X \rightarrow Y$ be a continuous mapping of a completely Baire space $X$ onto a hereditary weakly Preiss-Simon regular space $Y$ such that the image of every open subset of $X$ is a resolvable…
A topological space X$ has the Frechet-Urysohn property if for each subset A of X and each element x in the closure of A, there exists a countable sequence of elements of A which converges to x. Reznichenko introduced a natural…
For a free ultrafilter U on omega we study several cardinal characteristics which describe part of the combinatorial structure of U. We provide various consistency results; e.g. we show how to force simultaneously many characters and many…
Hindman's celebrated Finite Sums Theorem, and its high-dimensional version due to Milliken and Taylor, are extended from covers of countable sets to covers of arbitrary topological spaces with Menger's classic covering property. The methods…
We continue the exploration of various aspects of divisibility of ultrafilters, adding one more relation to the picture: multiplicative finite embeddability. We show that it lies between divisibility relations $\mid_M$ and…
A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces X which have the Hurewicz property…
The paper investigates the behavior of Hilbert-Samuel and Hilbert-Kunz multiplicities in families of ideals. It is shown that Hilbert-Samuel multiplicity is upper semicontinuous almost generally and that Hilbert-Kunz multiplicity is upper…
In this note, we characterize when the Vietoris space of compact subsets of a given space has the Hurewicz property in terms of a selection principle on the given space itself using $k$-covers and the notion of groupability introduced by…
W. Hurewicz proved that analytic Menger sets of reals are $\sigma$-compact and that co-analytic completely Baire sets of reals are completely metrizable. It is natural to try to generalize these theorems to projective sets. This has…
We introduce the natural and fairly general notion of a subanalytic bundle (with a finite dimensional vector space $P$ of sections) on a subanalytic subset $X$ of a real analytic manifold $M$, and prove that when $M$ is compact, there is a…
We study Baire category for subsets of 2^omega that are downward-closed with respect to the almost-inclusion ordering (on the power set of the natural numbers, identified with 2^omega). We show that it behaves better in this context than…
The product of a Sierpinski set and a Lusin set has Menger's property. The product of a gamma set and a Lusin set has Rothberger's property.
Let $U_l$ be a quantum group at an $l$th root of unity. Many tilting modules for $U_l$ have been shown to have what we call a balanced semisimple filtration, or a Loewy series whose semisimple layers are symmetric about some middle layer.…
The ultrafilters on the partial order $([\omega]^{\omega},\subseteq^*)$ are the free ultrafilters on $\omega$, which constitute the space $\omega^*$, the Stone-Cech remainder of $\omega$. If $U$ is an upperset of this partial order (i.e., a…
By classical results of Hurewicz, Kechris and Saint-Raymond, an analytic subset of a Polish space $X$ is covered by a $K_\sigma$ subset of $X$ if and only if it does not contain a closed-in-$X$ subset homeomorphic to the Baire space…
We present a study of semigroup compactifications of a semitopological semigroup $S$ using certain filters on $S$. We characterize closed subsemigroups and closed left, right, and two-sided ideals in any semigroup compactification of any…
We introduce a natural structure of a semigroup (isomorphic to a factorization semigroup of the unity in the symmetric group) on the set of irreducible components of Hurwitz space of marked degree $d$ coverings of $\mathbb P^1$ of fixed…