Related papers: Weak covering properties and selection principles
Inspired by a recent work of Dias and Tall, we show that a compact indestructible space is sequentially compact. We also prove that a Lindelof Hausdorff indestructible space has the finite derived set property and a compact Hausdorff…
A weakly complete space is a complex space admitting a (smooth) plurisubharmonic exhaustion function. In this paper, we classify those weakly complete complex surfaces for which such exhaustion function can be chosen real analytic: they can…
This paper presents a study of the inherent structural properties of Krylov subspaces, in particular for the self-adjoint class of operators, and how they relate with the important phenomenon of `Krylov solvability' of linear inverse…
We study linearly ordered spaces which are Valdivia compact in their order topology. We find an internal characterization of these spaces and we present a counter-example disproving a conjecture posed earlier by the first author. The…
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…
The paper deals with two issues: the existence of universal models of a theory T and related properties when cardinal arithmetic does not give this existence offhand. In the first section we prove that simple theories (e.g., theories…
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…
The two main results of this work are the following: if a space $X$ is such that player II has a winning strategy in the game $\gone(\Omega_x, \Omega_x)$ for every $x \in X$, then $X$ is productively countably tight. On the other hand, if a…
We construct a weakly compact convex subset of $\ell^2$ with nonempty interior that has an isolated maximal element, with respect to the lattice order $\ell _+^2$. Moreover, the maximal point cannot be supported by any strictly positive…
We define the notion of {\em classifying space} of a topological stack and show that every topological stack \X has a classifying space X which is a topological space well-defined up to weak homotopy equivalence. Under a certain…
We establish the choice property, a weak analogue of definable choice, for certain tame expansions of o-minimal structures. Most noteworthily, dense pairs of real closed fields have this property.
A typical result in this note is that if $X$ is a Banach space which is a weak Asplund space and has the $\omega^*$-$\omega$-Kadets Klee property, then $X$ is already an Asplund space.
We investigate preservation of the Lindel\"of property of topological spaces under forcing extensions. We give sufficient conditions for a forcing notion to preserve several strengthenings of the Lindel\"of property, such as indestructible…
The average result of a weak measurement of some observable $A$ can, under post-selection of the measured quantum system, exceed the largest eigenvalue of $A$. The nature of weak measurements, as well as the presence of post-selection and…
We discuss a natural topology on powers of a space that is inspired by the Vietoris topology on compact subsets. We then place this topology in context with other product topologies; specifically, we compare this topology with the Tychonoff…
We study the problem of existence of preduals of locally convex Hausdorff spaces. We derive necessary and sufficient conditions for the existence of a predual with certain properties of a bornological locally convex Hausdorff space $X$.…
If $X$ is a topological space and $\kappa$ is a cardinal then $\mathsf{BA}_\kappa (X)$ is the statement that for each pair $A, B \subseteq X$ of $\kappa$-dense subsets there is an autohomeomorphism $h:X \to X$ mapping $A$ to $B$. In…
Let M be a complete orientable manifold of bounded geometry. Suppose that M has finitely many ends, each having a neighborhood quasi-isometric to a neighborhood of an end of an infinite cyclic covering of a compact manifold. We consider a…
Class-conditional generative models hold promise to overcome the shortcomings of their discriminative counterparts. They are a natural choice to solve discriminative tasks in a robust manner as they jointly optimize for predictive…
We introduce and study weak o-minimality in the context of complete types in an arbitrary first-order theory. A type $p\in S(A)$ is weakly o-minimal if for some relatively $A$-definable linear order, $<$, on $p(\mathfrak{C})$ every…