Related papers: A note on Noetherian type of spaces

Let X be a zero-dimensional compact space such that all non-empty clopen subsets of X are homeomorphic to each other, and let H(X) be the group of all self-homeomorphisms of X with the compact-open topology. We prove that the Roelcke…

This paper is an erratum to our paper, entitled "On an application of Guth-Katz theorem", Math. Res. Lett. 18 (2011), no. 4, 691-697. Let $F$ be the real or complex field and $\omega$ a non-degenerate skew-symmetric bilinear form in the…

As it was introduced by Tkachuk and Wilson, a topological space $X$ is cellular-compact if given any cellular, i.e. disjoint, family $\mathcal U$ of non-empty open subsets of $X$ there is a compact subspace $K\subset X$ such that $K\cap…

Let T be the family of open subsets of a topological space (not necessarily Hausdorff or even T_0). We prove that if T has a base of cardinality <= mu, lambda <= mu < 2^lambda, lambda strong limit of cofinality aleph_0, then T has…

We give a new proof of the following theorem due to W. Weiss and P. Komjath: if $X$ is a regular topological space, with character $ < \mathfrak{b}$ and $X \rightarrow (top \omega + 1)^{1}_{\omega}$, then, for all $\alpha < \omega_1$, $X…

This paper addresses a conjecture of Kadison and Kastler that a von Neumann algebra M on a Hilbert space H should be unitarily equivalent to each sufficiently close von Neumann algebra N and, moreover, the implementing unitary can be chosen…

Given any commutative Noetherian ring $R$ and an element $x$ in $R$, we consider the full subcategory $\C(x)$ of its singularity category consisting of objects for which the morphism that is given by the multiplication by $x$ is zero. Our…

For a metrizable space $X$ of density $\kappa$, let $PM(X)$ be the space of continuous bounded pseudometrics on $X$ endowed with the uniform convergence topology. In this paper, its topology shall be classified as follows: (i) If $X$ is…

We construct a normal countably tight $T_1$ space $X$ with $t(X_\delta) >2^\omega$. This is an answer to the question posed by Dow-Juh\'asz-Soukup-Szentmikl\'ossy-Weiss. We also show that if the continuum is not so large, then the tightness…

We introduce and investigate a topological version of St\"ackel's 1907 characterization of finite sets, with the goal of obtaining an interesting notion that characterizes usual compactness (or a close variant of it). Define a $T_2$…

The property of countable metacompactness of a topological space gets its importance from Dowker's 1951 theorem that the product of a normal space X with the unit interval is again normal iff X is countably metacompact. In a recent paper,…

For a complex simple simply connected Lie group $G$, and a compact Riemann surface $C$, we consider two sorts of families of flat $G$-connections over $C$. Each family is determined by a point ${\mathbf u}$ of the base of Hitchin's…

Let $G$ be a finite group and $K$ a field containing an element of multiplicative order $|G|$. It is shown that if $G$ has a cyclic subgroup of index at most $2$, then the separating Noether number over $K$ of $G$ coincides with the Noether…

We prove that under [CH], finite compactifications of $\omega^* \setminus \{x\}$ are homeomorphic to $\omega^*$. Moreover, in each case, the remainder consists almost exclusively of $P$-points, apart from possibly one point. Similar results…

The gravitational Cheshire effect refers to the possibility of turning off the gravitational field while still leaving an imprint of the nonminimal coupling of matter to gravity. This allows nontrivial solutions in flat spacetime for which…

We prove that Alexandrov spaces $X$ of nonnegative curvature have Markov type 2 in the sense of Ball. As a corollary, any Lipschitz continuous map from a subset of $X$ into a 2-uniformly convex Banach space is extended as a Lipschitz…

Combining stationary reflection (a compactness property) with the failure of SCH (an instance of non-compactness) has been a long-standing theme. We obtain this at $\aleph_{\omega_1}$, answering a question of Ben-Neria, Hayut, and Unger: We…

Over these past few years several quantum-gravity research groups have been exploring the possibility that in some Planck-scale nonclassical descriptions of spacetime one or another form of nonclassical spacetime symmetries might arise. One…

Square-kappa-finite, the finite family version of weak square, holds at all cardinals kappa in the Mitchell-Steel inner models.

We consider $L$-$\omega$-nonexpansive maps $T\colon K\to K$ on a convex subset $K$ of a Banach space $X$, i.e., maps in which $\omega_T(\delta)\leq L\delta +\omega(\delta)$ with $L\in [0,1]$, $\omega$ being a modulus of continuity and…