Related papers: On feebly compact semitopological semilattice $\ex…

We study the model theoretic strength of various lattices that occur naturally in topology, like closed (semi-linear or semi-algebraic or convex) sets. The method is based on weak monadic second order logic and sharpens previous results by…

We show that any diffeomorphism of a compact manifold can be C1 approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.

In this paper, some characterizations about transitivity, mildly mixing property, $\mathbf{a}$-transitivity, equicontinuity, uniform rigidity and proximality of Zadeh's extensions restricted on some invariant closed subsets of the space of…

A space is od-compact (resp. od-Lindel\"of) provided any cover by open dense sets has a finite (resp. countable) subcover. We first show with simple examples that these properties behave quite poorly under finite or countable unions. We…

We survey recent lattice results on QCD topological properties. The behaviour of the topological susceptibility at the deconfining phase transition has been determined. This advance has been made possible by an i) an improvement of the…

Let $G$ be a group hyperbolic relative to a finite collection of subgroups $\mathcal P$. Let $\mathcal F$ be the family of subgroups consisting of all the conjugates of subgroups in $\mathcal P$, all their subgroups, and all finite…

We prove that every distributive algebraic lattice with at most $\aleph\_1$ compact elements is isomorphic to the normal subgroup lattice of some group and to the submodule lattice of some right module. The $\aleph\_1$ bound is optimal, as…

Suppose $G$ is a higher-rank connected semisimple Lie group with finite center and without compact factors. Let $\mathbb{G}=G$ or $\mathbb{G}=G\ltimes V$, where $V$ is a finite dimensional vector space $V$. For any unitary representation…

We consider the lattice topological charge density introduced by Hasenfratz, Laliena and Niedermayer and propose its eigenmode expansion as a tool to investigate the structure of topological charge fluctuations in QCD. The resulting…

McLean studied the deformations of compact special Lagrangian submanifolds, showing in particular that they come in moduli spaces whose dimension depends only on the topology of the submanifold. In this article we study the analogous…

Let $G$ be a group and $\sigma, \tau$ be topological group topologies on $G$. We say that $\sigma$ is a successor of $\tau$ if $\sigma$ is strictly finer than $\tau$ and there is not a group topology properly between them. In this note, we…

Using a reweighting technique combined with a low-mode truncation of the fermionic determinant, we estimate the quark-mass dependence of the QCD topological susceptibility with overlap fermions. In contrast to previous lattice simulations…

We prove that every compact complex surface with odd first Betti number admits a locally conformally symplectic $2$-form which tames the underlying almost complex structure.

Let $\mathfrak{P}$ be a topological property. We study the relation between the order structure of the set of all $\mathfrak{P}$-extensions of a completely regular space $X$ with compact remainder (partially ordered by the standard partial…

We prove that many completeness properties coincide in metric spaces, precompact groups and dense subgroups of products of separable metric groups. We apply these results to function spaces C_p(X,G) of G-valued continuous functions on a…

In this expository article, we give a self-contained introduction to the wonderfully well-behaved class of pseudocompact algebras, focusing on the foundational classes of semisimple and separable algebras. We give characterizations of such…

We study deformations of symplectic structures on a smooth manifold $M$ via the quasi-Poisson theory. By a fact, we can deform a given symplectic structure $\omega $ to a new symplectic structure $\omega_t$ parametrized by some element $t$…

We investigate closed subsets (subsemigroups, resp.) of compact-like topological spaces (semigroups, resp.). We prove that each Hausdorff topological space can be embedded as a closed subspace into an H-closed topological space. However,…

We prove that, for an arbitrary topological space $X$, the following two conditions are equivalent: (a) Every open cover of $X$ has a finite subset with dense union (b) $X$ is $D$-pseudocompact, for every ultrafilter $D$. Locally, our…

We introduce the notion of topological electronic states on random lattices in non-integer dimensions. By considering a class $D$ model on critical percolation clusters embedded in two dimensions, we demonstrate that these topological…