Related papers: What makes a space have large weight?
This paper addresses several questions of Feng, Gruenhage, and Shen which arose from Michael's theory of continuous selections from countable spaces. We construct an example of a space which is $L$-selective but not $\mathbb{Q}$-selective…
We define several notions of a limit point on sequences with domain a barrier in $[\omega]^{<\omega}$ focusing on the two dimensional case $[\omega]^2$. By exploring some natural candidates, we show that countable compactness has a number…
In this paper, some features of countably $\alpha$-compact topological spaces are presented and proven. The connection between countably $\alpha$% -compact, Tychonoff, and $\alpha$-Hausdorff spaces is explained. The space is countably…
We build an example of a metric space with transfinite asymptotic dimension $2\omega$.
A metric space is said to be strongly rigid if no positive distance is taken twice by the metric. In 1972, Janos proved that a separable metrizable space has a strongly rigid metric if and only if it is zero-dimensional. In this paper, we…
We continue here [She88] but we do not rely on it. The motivation was a conjecture of Galvin stating that 2^{omega} >= omega_2 + omega_2-> [omega_1]^{n}_{h(n)} is consistent for a suitable h: omega-> omega. In section 5 we disprove this and…
We show that it is relatively consistent with ZFC that 2^omega is arbitrarily large and every sequence s=(s_i:i<omega_2) of infinite cardinals with s_i<=2^omega is the cardinal sequence of some locally compact scattered space.
For each countable ordinal $\alpha$ let $\mathcal{S}_{\alpha}$ be the Schreier set of order $\alpha$ and $X_{\mathcal{S}_\alpha}$ be the corresponding Schreier space of order $\alpha$. In this paper we prove several new properties of these…
This paper is devoted to the study of the weighted Bergman space $A_\omega^p $ in the unit ball $\mathbb{B}$ of $\mathbb{C}^n$ with doubling weight $\omega$ satisfying $$\int_r^1\omega(t)dt <C \int_{\frac{1+r}{2}}^1\omega(t)dt ,\,\, 0\leq…
We show that an inhomogeneous compact extra space possesses two necessary features --- their existence does not contradict the observable value of the cosmological constant $\Lambda_4$ in pure $f(R)$ theory, and the extra dimensions are…
There is now strong evidence that the main contribution to the cosmic energy density is not due to matter, but to another component with negative pressure. Its nature is still unknown: it could be the vacuum energy, manifesting itself as a…
We try to build, provably in ZFC, for a first order T a model in which any isomorphism between two Boolean algebras is definable. The problem, compared to [Sh:384], is with pseudo-finite Boolean algebras. A side benefit is that we do not…
The hypothesis is made that, at large scales where General Relativity may be applied, the empty space is scale invariant. This establishes a relation between the cosmological constant and the scale factor of the scale invariant framework.…
A topological space $X$ is called strongly $\sigma$-metrizable if $X=\bigcup_{n\in\omega}X_n$ for an increasing sequence $(X_n)_{n\in\omega}$ of closed metrizable subspaces such that every convergence sequence in $X$ is contained in some…
We first introduce and study two new classes of subsets in $T_0$ spaces - $\omega$-Rudin sets and $\omega$-well-filtered determined sets lying between the class of all closures of countable directed subsets and that of irreducible closed…
Chang's Conjecture (CC) asserts that for every $F:[\omega_2]^{<\omega} \to \omega_2$, there exists an $X$ that is closed under $F$ such that $|X|=\omega_1$ and $|X \cap \omega_1| =\omega$. By classic results of Silver and Donder, CC is…
It is known due to the work of Van den Broeck et al [KR, 2014] that weighted first-order model counting (WFOMC) in the two-variable fragment of first-order logic can be solved in time polynomial in the number of domain elements. In this…
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…
We introduce a general method of constructing locally compact scattered spaces from certain families of sets and then, with the help of this method, we prove that if kappa^{<kappa}=kappa then there is such a space of height kappa^+ with…
Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties themselves and processes which carry out the verification…