Related papers: On a problem of Angelo Bella

It is an interesting, maybe surprising, fact that different dense subspaces of even "nice" topological spaces can have different densities. So, our aim here is to investigate the set of densities of all dense subspaces of a topological…

A space $X$ is said to be "cellular-Lindel\"of" if for every cellular family $\mathcal{U}$ there is a Lindel\"of subspace $L$ of $X$ which meets every element of $\mathcal{U}$. Cellular-Lindel\"of spaces generalize both Lindel\"of spaces…

Given a module $X$ and a regular cardinal $\kappa$ we study various notions of $(\kappa,\mathrm{Add}(X))$-freeness and $(\kappa,\mathrm{Add}(X))$-separability. Bearing on appropriate set-theoretic assumptions, we construct a non-trivial…

We study the relations between a generalization of pseudocompactness, named $(\kappa, M)$-pseudocompactness, the countably compactness of subspaces of $\beta \omega$ and the pseudocompactness of their hyperspaces. We show, by assuming the…

A topological space $X$ is a $\Delta$-space (or $X \in \Delta$) if for any decreasing sequence $\{A_n : n < \omega\}$ of subsets of $X$ with empty intersection there is a (decreasing) sequence $\{U_n : n < \omega\}$ of open sets with empty…

We prove a Kawamata-Viehweg vanishing theorem on a normal compact Kahler space X: if L is a nef line bundle with numerical dimension at least equal to 2, then the q-th cohomology group of K_X+L vanishes for q at least equal to the dimension…

An open chain cover $\{U_\alpha : \alpha\in\kappa\}$ ($\kappa$ a cardinal) of a space $X$ is a systematic cover if the closure of $U_\alpha$ is contained in $U_\beta$ when $\alpha<\beta$, and $X$ is Type I if $\kappa=\omega_1$ and the…

We say that a Tychonoff space $X$ is a $\kappa$-space if it is homeomorphic to a closed subspace of $C_p(Y)$ for some locally compact space $Y$. The class of $\kappa$-spaces is strictly between the class of Dieudonn\'{e} complete spaces and…

Given a Banach space we consider the $\sigma$-ideal of all of its subsets which are covered by countably many hyperplanes and investigate its standard cardinal characteristics as the additivity, the covering number, the uniformity, the…

The $G_\delta$-modification $X_\delta$ of a topological space $X$ is the space on the same underlying set generated by, i.e. having as a basis, the collection of all $G_\delta$ subsets of $X$. Bella and Spadaro recently investigated the…

We present a bound for the weak Lindel\"of number of the $G_\delta$-modification of a Hausdorff space which implies various known cardinal inequalities, including the following two fundamental results in the theory of cardinal invariants in…

The weak tightness $wt(X)$, introduced in [6], has the property $wt(X)\leq t(X)$. It was shown in [4] that if $X$ is a homogeneous compactum then $|X|\leq 2^{wt(X)\pi\chi(X)}$. We introduce the almost tightness $at(X)$ with the property…

Assume hat a functionally Hausdorff space $X$ is a continuous image of a \v{C}ech complete space $P$ with Lindel\"of number $l(P)<\mathfrak c$. Then the following conditions are equivalent: (i) every compact subset of $X$ is scattered, (ii)…

Say that a cardinal number $\kappa$ is \emph{small} relative to the space $X$ if $\kappa <\Delta(X)$, where $\Delta(X)$ is the least cardinality of a non-empty open set in $X$. We prove that no Baire metric space can be covered by a small…

Sapirovskii [18] proved that $|X|\leq\pi\chi(X)^{c(X)\psi(X)}$, for a regular space $X$. We introduce the $\theta$-pseudocharacter of a Urysohn space $X$, denoted by $\psi_\theta (X)$, and prove that the previous inequality holds for…

We solve a long standing question due to Arhangel'skii by constructing a compact space which has a $G_\delta$ cover with no continuum-sized ($G_\delta$)-dense subcollection. We also prove that in a countably compact weakly Lindel\"of normal…

For a Hausdorff topologized semilattice $X$ its $Lawson\;\; number$ $\bar\Lambda(X)$ is the smallest cardinal $\kappa$ such that for any distinct points $x,y\in X$ there exists a family $\mathcal U$ of closed neighborhoods of $x$ in $X$…

A space $X$ is of countable type (resp. subcountable type) if every compact subspace $F$ of $X$ is contained in a compact subspace $K$ that is of countable character (resp. countable pseudocharacter) in $X$. In this paper, we mainly show…

A Hausdorff topological group G is minimal if every continuous isomorphism f : G --> H between G and a Hausdorff topological group H is open. Clearly, every compact Hausdorff group is minimal. It is well known that every infinite compact…

A space X is kappa-resolvable (resp. almost kappa-resolvable) if it contains kappa dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets of X). Answering a problem raised by Juhasz, Soukup, and…