Related papers: On spaces with star kernel Menger
In this paper, we investigate what selection principles properties are possessed by small (with respect to the bounding and dominating numbers) unions of spaces with certain (star) selection principles.. Furthermore, we give several results…
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 space $X$ is od-Menger if it satisfies $\mathsf{U_{fin}}(\Delta_X, \mathcal{O}_X)$, where $\mathcal{O}_X,\Delta_X$ are the collection of covers of $X$ by respectively open subsets and open dense subsets. We show that under CH, there is a…
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…
A space $X$ is said to have the set star Hurewicz property if for each nonempty subset $A$ of $X$ and each sequence $(\mathcal{U}_n: n \in \mathbb{N})$ of sets open in $X$ such that for each $n\in \mathbb N$, $\overline{A} \subset \cup…
For a Tychonoff space $X$ and a family $\lambda$ of subsets of $X$, we denote by $C_{\lambda}(X)$ the space of all real-valued continuous functions on $X$ with the set-open topology. In this paper, we study the Menger and projective Menger…
A space $ X $ is said to be set star-Lindel\"{o}f (resp., set strongly star-Lindel\"{o}f) if for each nonempty subset $ A $ of $ X $ and each collection $ \mathcal{U} $ of open sets in $ X $ such that $ \overline{A} \subseteq \bigcup…
The main results of this note are: It is consistent that every subparacompact space $X$ of size $\omega_1$ is a $D$-space; If there exists a Michael space, then all productively Lindel\"of spaces have the Menger property, and, therefore,…
We investigate star-covering properties of $\Psi$-like spaces. We show star-Lindel\"ofness is reflected by open perfect mappings. In addition, we offer a new equivalence of CH.
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…
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…
Which Isbell--Mr\'owka spaces ($\Psi$-spaces) satisfy the star version of Menger's and Hurewicz's covering properties? Following Bonanzinga and Matveev, this question is considered here from a combinatorial point of view. An example of a…
Let $\mathcal{W}^{n}$ be the class of $C^{\infty }$ complete simply connected $n-$dimensional manifolds without conjugate points. The hyperbolic space as well as Euclidean space are good examples of such manifolds. Let $% W\in…
We study the relation between the Hurewicz and Menger properties of filters considered topologically as subspaces of P(\omega) with the Cantor set topology.
A set is star-shaped if there is a point in the set that can see every other point in the set in the sense that the line-segment connecting the points lies within the set. We show that testing whether a non-empty compact smooth region is…
In this paper, the author first establish the connections between the selectively $k$-star-ccc properties, the chain conditions and other star-Lindel\"of properties. Secondly, some examples are presented to solve questions raised by Xuan…
In this paper, the author represent a unification and extension of concepts previously studied by several authors. By establish connections between the chain condition, selectively star-ccc properties and star-Lindel\"of properties, the…
A topological space is totally paracompact if any base of this space contains a locally finite subcover. We focus on a problem of Curtis whether in the class of regular Lindel\"of spaces total paracompactness is equivalent to the Menger…
Uniformly star superparacompactness, which is a topological property between compactness and completeness, can be characterized using finite-component covers and a measure of strong local compactness. Using these finite-component covers and…
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…