Related papers: Digging into the classes of $\kappa$-Corson compac…

For each cardinal $\kappa$, each natural number $n$ and each simplicial complex $K$ we construct a space $\nu^n_\kappa(K)$ and a map $\pi \colon \nu^n_\kappa(K) \to K$ such that the following conditions are satisfied. 1. $\nu^n_\kappa(K)$…

Let $K$ be a global field of characteristic $p>0$. We study the cohomology of arithmetic subgroups $\Gamma $ of $SL_{n+1}(K)$ (with respect to a fixed place of $K$), under the hypothesis that these groups have no $p'$-torsion (any…

We show that for any uncountable cardinal $\lambda$, the category of sets of cardinality at least $\lambda$ and monomorphisms between them cannot appear as the category of point of a topos, in particular is not the category of models of a…

We show, assuming the consistency of one measurable cardinal, that it is consistent for there to be exactly kappa+ many normal measures on the least measurable cardinal kappa. This answers a question of Stewart Baldwin. The methods…

Let $X$ be a product of locally compact rank one Hadamard spaces and $\Gamma$ a discrete group of isometries which contains two elements projecting to a pair of independent rank one isometries in each factor. In [arXiv:1308.5584] we gave a…

Building on work of Holy, L\"ucke and Njegomir \cite{MR3913154} on small embedding characterizations of large cardinals, we use some classical results of Baumgartner (see \cite{MR0384553} and \cite{MR0540770}), to give characterizations of…

The $\kappa$-topologies on the spaces $\mathscr{D}_{L^p}$, $L^p$ and $\mathscr{M}^1$ are defined by a neighbourhood basis consisting of polars of absolutely convex and compact subsets of their (pre-)dual spaces. In many cases it is more…

We show that all sufficiently nice $\lambda$-sets are countable dense homogeneous ($\mathsf{CDH}$). From this fact we conclude that for every uncountable cardinal $\kappa \le \mathfrak{b}$ there is a countable dense homogeneous metric space…

We prove that for any regular kappa and mu > kappa below the first fix point (lambda = aleph_lambda) above kappa, there is a graph with chromatic number > kappa, and mu^kappa nodes but every subgraph of cardinality < mu has chromatic number…

We obtain a simple, recursive presentation of the tautological (\kappa, \psi, and \lambda) classes on the moduli space of curves in genus zero and one in terms of boundary strata (graphs). We derive differential equations for the generating…

Some new classes of compacta $K$ are considered for which $C(K)$ endowed with the pointwise topology has a countable cover by sets of small local norm--diameter.

Assuming an instance of the Brodsky-Rinot proxy principle holding at a regular uncountable cardinal $\kappa$, we construct $2^\kappa$-many pairwise non-embeddable minimal non-$\sigma$-scattered linear orders of size $\kappa$. In particular,…

Being motivated by the notions of $\kappa$-Fr\'{e}chet--Urysohn spaces and $k'$-spaces introduced by Arhangel'skii, the notion of sequential spaces and the study of Ascoli spaces, we introduce three new classes of compact-type spaces. They…

Let $\Gamma$ be a Polish space and let $K$ be a separable and pointwise compact set of real-valued functions on $\Gamma$. It is shown that if each function in $K$ has only countably many discontinuities then $C(K)$ may be equipped with a…

In the paper, we investigate (scattered) compact spaces with a $P$-base for some poset $P$. More specifically, we prove that, under the assumption $\omega_1<\mathfrak{b}$, any compact space with an $\omega^\omega$-base is first-countable…

Let $G$ be an infinite group, $\kappa$ be an infinite cardinal, $\kappa\leq \mid G\mid$ and let $\mathcal{E}_{\kappa}$ denotes a coarse structure on $G$ with the base $\{\{ (x,y): y\in F x F\}: F\in [G]^{<\kappa}\}$. We prove that if either…

For $n<\omega$, we say that the $\Pi^1_n$-reflection principle holds at $\kappa$ and write $\text{Refl}_n(\kappa)$ if and only if $\kappa$ is a $\Pi^1_n$-indescribable cardinal and every $\Pi^1_n$-indescribable subset of $\kappa$ has a…

We show that $X^\lambda$ is strongly homogeneous whenever $X$ is a non-separable zero-dimensional metrizable space and $\lambda$ is an infinite cardinal. This partially answers a question of Terada, and improves a previous result of the…

We introduce a generalization of sequential compactness using barriers on $\omega$ extending naturally the notion introduced in [W. Kubi\'{s} and P. Szeptycki, On a topological Ramsey theorem, \emph{Canad. Math. Bull.}, 66 (2023),…

In the context of large cardinals, the classical diamond principle Diamond_kappa is easily strengthened in natural ways. When kappa is a measurable cardinal, for example, one might ask that a Diamond_kappa sequence anticipate every subset…