相关论文: On Traditional Menger and Rothberger Variations
We study the relation between the Hurewicz and Menger properties of filters considered topologically as subspaces of P(\omega) with the Cantor set topology.
In this paper we construct consistent examples of subgroups of $2^\omega$ with Menger remainders which fail to have other stronger combinatorial covering properties. This answers several open questions asked by Bella, Tokgoz and Zdomskyy…
In this paper we give the functional characteristics of the Rothberger and Menger properties.
We provide new results on combinatorial characterizations of covering properties in end spaces and ray spaces. In particular, we characterize the Lindel\"of degree, the extent, the Rothberger property, $\sigma$-compactness and the Menger…
We characterize various Menger/Rothberger related properties by means of ultrafilter convergence, and discuss their behavior with respect to products.
We characterize exactly the compactness properties of the product of \kappa\ copies of the space \omega\ with the discrete topology. The characterization involves uniform ultrafilters, infinitary languages, and the existence of nonstandard…
In this paper we introduce and study the local version of the Menger property, namely locally Menger property (or, locally Menger space). We explore some preservation like properties in this space. We also discuss certain situations where…
We describe some of the connections between the Bieri-Neumann-Strebel-Renz invariants, the Dwyer-Fried invariants, and the cohomology support loci of a space X. Under suitable hypotheses, the geometric and homological finiteness properties…
In this paper we define some combinatorial principles to characterize spaces $X$ whose hyperspace satisfies some variation of some classical star selection principle. Specifically, the variations characterized are the selective and absolute…
We study tightness properties and selective versions of separability in bitopological function spaces endowed with set-open topologies.
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…
We suggest to look at formal sentences describing complex algebraic varieties together with their universal covers as topological invariants. We prove that for abelian varieties and Shimura varieties this is indeed a complete invariant,…
Let O be a complete discrete valuation ring of mixed characteristic and with finite residue field k. We study a natural morphism between the Greenberg algebra of O and the special fiber of the scheme of ramified Witt vectors over O. It is a…
We continue to investigate various diagonalization properties for sequences of open covers of separable metrizable spaces introduced in Part I. These properties generalize classical ones of Rothberger, Menger, Hurewicz, and Gerlits-Nagy. In…
In this paper we discuss what kind of constrains combinatorial covering properties of Menger, Scheepers, and Hurewicz impose on remainders of topological groups. For instance, we show that such a remainder is Hurewicz if and only it is…
We characterize the compactness properties of the product of \lambda\ copies of the space \omega\ with the discrete topology, dealing in particular with the case \lambda\ singular, using regular and uniform ultrafilters, infinitary…
A reduction of properties (invariants) of compact sets of real numbers to properties of countable orders is presented here. Discussed here is also an embedding property of some compact sets that are called t$\mathbb R$-sets. Among others,…
We review some selected recent results concerning selection principles in topology and their relations with several topological constructions.
We give conditions under which a product of topological spaces satisfies some local property. The conditions are necessary and sufficient when the corresponding global property is preserved under finite products. Further examples include…
We continue to investigate applications of $k$-covers in function spaces with the compact-open topology.