Related papers: The completeness of free Boolean topological group…

A topological group $G$ is {\em sequentially $h$-complete} if all the continuous homomorphic images of $G$ are sequentially complete. In this paper we give necessary and sufficient conditions on a complete group for being compact, using the…

A strongly zero-dimensional topological group containing a closed subgroup of positive covering dimension is constructed.

This paper shows that for K a local field, k a subfield of K and X a variety over k, X is complete if and only if for every finite field extension K' of K, X(K') is compact in its strong topology.

Recall that a space X is selectively pseudocompact if for every sequence (U_n) of non-empty open subsets of X one can choose a point x_n in U_n for all n such that the resulting sequence (x_n) has an accumulation point in X. This notion was…

Given an action $G \curvearrowright X$ of a discrete and countable infinite group $G$ on a compact and Hausdorff space $X$, we regard $\ell^1(G\curvearrowright X)$ as the Banach *-algebra crossed product associated to the action. We…

Let $G$ be a finite group and $S$ a subset of $G$. Then $S$ is product-free if $S \cap SS = \emptyset$, and complete if $G^{\ast} \subseteq S \cup SS$. A product-free set is locally maximal if it is not contained in a strictly larger…

We prove a few basic facts about the space of bi-invariant (or left-invariant) total order relations on a torsion-free, nonabelian, nilpotent group G. For instance, we show that the space of bi-invariant orders has no isolated points (so it…

We extend the definition of Bockstein basis $\sigma(G)$ to nilpotent groups $G$. A metrizable space $X$ is called a {\it Bockstein space} if $\dim_G(X) = \sup\{\dim_H(X) | H\in \sigma(G)\}$ for all Abelian groups $G$. Bockstein First…

The path component space of a topological space $X$ is the quotient space $\pi_0(X)$ whose points are the path components of $X$. We show that every Tychonoff space $X$ is the path-component space of a Tychonoff space $Y$ of weight…

For a marked point process $\{(x_i,S_i)_{i\geq 1}\}$ with $\{x_i\in \Lambda:i\geq 1\}$ being a point process on $\Lambda \subseteq \mathbb{R}^d$ and $\{S_i\subseteq R^d:i\geq 1\}$ being random sets consider the region $C=\cup_{i\geq…

We give a counterexample to a conjecture by Miasnikov, Ventura and Weil, stating that an extension of free groups is algebraic if and only if the corresponding morphism of their core graphs is onto, for every basis of the ambient group. In…

Let $\mbox{TFAG}$ be the theory of torsion-free abelian groups. We show that if there is no countable transitive model of $ZFC^- + \kappa(\omega)$ exists, then $\mbox{TFAG}$ is $a \Delta^1_2$-complete; in particular, this is consistent with…

We show that it is consistent with ZFC (relative to large cardinals) that every infinite Boolean algebra B has an irredundant subset A such that 2^{|A|} = 2^{|B|}. This implies in particular that B has 2^{|B|} subalgebras. We also discuss…

We study when a map between two subsets of a Boolean domain W can be extended to an automorphism of W. Under many hypotheses, if the underlying Boolean algebra is complete or if the sets are finite or Boolean domains, the necessary and…

We present sufficient conditions for the triviality of the automorphism group of regular Toeplitz subshifts and give a broad class of examples from the class of $\mathcal{B}$-free subshifts satisfying them, extending [10]. On the other hand…

Let $\mathcal{G}_{\alpha}(X, G)$ be the $G$-gauge group over a space $X$ corresponding to a map $\alpha \colon X \to BG$. We compute the integral cohomology of $B\mathcal{G}_{1}(S^2, SO(n))$ for $n = 3,4$. We also show that the homology of…

Suppose that G is a nontrivial torsion-free group and w is a word over the alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\}. It is proved that for n\ge2 the group \~G=<G,x_1,x_2,...,x_n | w=1> always contains a nonabelian free subgroup. For n=1…

We consider the quantifier-free languages, Bc and Bc0, obtained by augmenting the signature of Boolean algebras with a unary predicate representing, respectively, the property of being connected, and the property of having a connected…

Recently Au\ss enhofer and the author independently have shown that the free abelian topological group $A(\mathbf{s})$ over a convergent sequence $\mathbf{s}$ does not admit the strongest compatible locally quasi-convex group topology that…

Given a complete Heyting algebra we construct an algebraic tensor triangulated category whose Bousfield lattice is the Booleanization of the given Heyting algebra. As a consequence we deduce that any complete Boolean algebra is the…