Related papers: Weakly separated spaces and Pixley-Roy hyperspaces

We give several new bounds for the cardinality of a Hausdorff topological space $X$ involving the weak Lindel\"of degree $wL(X)$. In particular, we show that if $X$ is extremally disconnected, then $|X|\leq 2^{wL(X)\pi\chi(X)\psi(X)}$, and…

We give a general closing-off argument in Theorem 2.1 from which several corollaries follow, including (1) if $X$ is a locally compact Hausdorff space then $|X|\leq 2^{wL(X)\psi(X)}$, and (2) if $X$ is a locally compact power homogeneous…

We call a space $X$ {\it weakly linearly Lindel\"of} if for any family $\mathcal{U}$ of non-empty open subsets of $X$ of regular uncountable cardinality $\kappa$, there exists a point $x\in X$ such that every neighborhood of $x$ meets…

Let $X$ be a Hausdorff space and let $\mathcal{H}$ be one of the hyperspaces $CL(X)$, $\mathcal{K}(X)$, $\mathcal{F}(X)$ or $\mathcal{F}_n(X)$ ($n$ a positive integer) with the Vietoris topology. We study the following disconnectedness…

Motivated by results of Juh\'asz and van Mill in [13], we define the cardinal invariant $wt(X)$, the weak tightness of a topological space $X$, and show that $|X|\leq 2^{L(X)wt(X)\psi(X)}$ for any Hausdorff space $X$ (Theorem 2.8). As…

For a Urysohn space $X$ we define the regular diagonal degree $\overline{\Delta}(X)$ of $X$ to be the minimal infinite cardinal $\kappa$ such that $X$ has a regular $G_\kappa$-diagonal i.e. there is a family $(U_\eta:\eta<\kappa)$ of open…

The weak Whyburn property is a generalization of the classical sequential property that has been studied by many authors. A space $X$ is weakly Whyburn if for every non-closed set $A \subset X$ there is a subset $B \subset A$ such that…

A topological space $X$ is called hereditarily supercompact if each closed subspace of X is supercompact. By a combined result of Bula, Nikiel, Tuncali, Tymchatyn, and Rudin, each monotonically normal compact Hausdorff space is hereditarily…

Orderability, weak orderability and the existence of continuous weak selections on filter spaces (i.e., spaces with a single non-isolated point) and their products are discussed. We prove that a closed continuous image X of a suborderable…

We strengthen the property $\Delta$ of a function $f:[\omega_2]^2\rightarrow [\omega_2]^{\leq \omega}$ considered by Baumgartner and Shelah. This allows us to consider new types of amalgamations in the forcing used by Rabus, Juh\'asz and…

We show that if $X$ has a zero-set diagonal and $X^2$ has countable weak extent, then $X$ is submetrizable. This generalizes earlier results from Martin and Buzyakova. Furthermore we show that if $X$ has a regular $G_\delta$-diagonal and…

In this paper, we investigate various cardinal properties of the space $Q_{C}X$ of all real-valued quasicontinuous functions on the topological space $X$, under the topology of uniform convergence on compact subsets. It begins by examining…

A dual pair formulation for asymmetric locally convex spaces is developed that strictly generalises the ordinary vector space setting. The concept of a polar topology carries over to the asymmetric case and some familiar results are…

We define a topological space to be an "SDL space" if the closure of each one of its strongly discrete subsets is Lindel\"of. After distinguishing this property from the Lindel\"of property we make various remarks about cardinal invariants…

A topological space $X$ is $strongly$ $rigid$ if each non-constant continuous map $f:X\to X$ is the identity map of $X$. A Hausdorff topological space $X$ is called $Brown$ if for any nonempty open sets $U,V\subseteq X$ the intersection…

Let $X$ be a Banach space and $Y \subseteq X$ be a closed subspace. We prove that if the quotient $X/Y$ is weakly Lindel\"{o}f determined or weak Asplund, then for every $w^*$-convergent sequence $(y_n^*)_{n\in \mathbb N}$ in $Y^*$ there…

The "weakly Hausdorff" property for pseudoradial spaces fails to be naturally characterized by unique convergence of transfinite sequences. In response, we develop the category $\mathbf{SPsRad}$ of strongly pseudoradial spaces, compactly…

We show that all finite powers of a Hausdorff space X do not contain uncountable weakly separated subspaces iff there is a c.c.c poset P such that 1_P forces that ``X is a countable union of 0-dimensional subspaces of countable weight.'' We…

If $f$ is a real valued weakly lower semi-continous function on a Banach space $X$ and $C$ a weakly compact subset of $X$, we show that the set of $x \in X$ such that $z \mapsto \|x-z\|-f(z)$ attains its supremum on $C$ is dense in $X$. We…

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)…