相关论文: First countable spaces without point-countable $\p…
Let $\kappa$ be an infinite cardinal. A topological space $X$ is $\kappa$-bounded if the closure of any subset of cardinality $\le\kappa$ in $X$ is compact. We discuss the problem of embeddability of topological spaces into Hausdorff…
In this paper we prove that if $\kappa$ is a singular cardinal with uncountable cofinality, then every power of a given topological space with precaliber $\kappa$ has precaliber $\kappa$ as well. Furthermore, if $\{X_\alpha :…
This article examines Hilbert spaces constructed from sets whose existence is incompatible with the Countable Axiom of Choice (CC). Our point of view is twofold: (1) We examine what can and cannot be said about Hilbert spaces and operators…
We show that there are uncountably many mutually non-isomorphic Lipschitz-free spaces over countable, complete, discrete metric spaces. Also there is a countable, complete, discrete metric space whose free space does not embed into the free…
A matching prior at level $1-\alpha$ is a prior such that an associated $1-\alpha$ credible set is also a $1-\alpha$ confidence set. We study the existence of matching priors for general families of credible regions. Our main result gives…
In the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $\mathbf{ZF}$, some are shown to be independent of…
A. V. Arhangel'ski\u{i} introduced in 2012, when he was visiting the department of Mathematics at King Abduaziz University, new weaker versions of normality, called \it $C$-normality, \rm and \it countable normality. \rm The purpose of this…
Let kappa be a regular uncountable cardinal and lambda >=kappa^+ . The principle of stationary reflection for P_kappa lambda has been successful in settling problems of infinite combinatorics in the case kappa=omega_1. For a greater kappa…
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)…
In computable analysis typically topological spaces with countable bases are considered. The Theorem of Kreitz-Weihrauch implies that the subbase representation of a second-countable $T_0$ space is admissible with respect to the topology…
We prove that a Hausdorff space $X$ is very $\mathrm I$-favorable if and only if $X$ is the almost limit space of a $\sigma$-complete inverse system consisting of (not necessarily Hausdorff) second countable spaces and surjective d-open…
We continue our investigation of cardinal sequences associated with locally Lindelof, scattered, Hausdorff P-spaces (abbreviated as LLSP spaces). We outline a method for constructing LLSP spaces from cone systems and partial orders with…
The Hanf number for a set $S$ of sentences in $L_{\omega_1,\omega}$ (or some other logic) is the least infinite cardinal $\kappa$ such that for all $\varphi\in S$, if $\varphi$ has models in all infinite cardinalities less than $\kappa$,…
A result of Kaufmann shows that if $L_\alpha$ is countable, admissible and satisfies $\Pi_n\textsf{-Collection}$, then $\langle L_\alpha, \in \rangle$ has a proper $\Sigma_{n+1}$-elementary end extension. This paper investigates to what…
In a previous work, the first named author described the set $\cal P$ of all values of the Szlenk indices of separable Banach spaces. We complete this result by showing that for any integer $n$ and any ordinal $\alpha$ in $\cal P$, there…
This article continues the study of computable elementary topology started by the author and T. Grubba in 2009 and extends the author's 2010 study of axioms of computable separation. Several computable T3- and Tychonoff separation axioms…
The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskii, Tseitin, Kreisel, and Lacombe assert the existence of NON-empty co-r.e. closed sets devoid of computable points: sets which are…
The topological fundamental group $\pi_{1}^{top}$ is a homotopy invariant finer than the usual fundamental group. It assigns to each space a quasitopological group and is discrete on spaces which admit universal covers. For an arbitrary…
This note provides a correct proof of the result claimed by the second author that locally compact normal spaces are collectionwise Hausdorff in certain models obtained by forcing with a coherent Souslin tree. A novel feature of the proof…
We construct a space ${X}$ that has a Lusin $\pi$-base and such that ${X}^{2}$ has no Lusin $\pi$-base.