Related papers: A counterexample for a suptheorem in locally conve…

We consider pseudoconvexity properties in Lorentzian and Riemannian manifolds and their relationship in static spacetimes. We provide an example of a causally continuous and maximal null pseudoconvex spacetime that fails to be causally…

We introduce moment maps for continuous unitary representations of general topological groups. For solvable separable locally compact groups, we prove that the closure of the image of the moment map of any representation is convex.

We generalize a result of Serre's to show that if every vertex of some fixed type of a convex subcomplex of an irreducible spherical building has an opposite, then the subcomplex is completely reducible.

In recent work by Zimmer it was proved that if $\Omega\subset\mathbb C^n$ is a bounded convex domain with $C^\infty$-smooth boundary, then $\Omega$ is strictly pseudoconvex provided that the squeezing function approaches one as one…

We prove that any continuous mapping $f:E\to Y$ on a completely metrizable subspace $E$ of a perfect paracompact space $X$ can be extended to a Lebesgue class one mapping $g:X\to Y$ (i.e. for every open set $V$ in $Y$ the preimage…

In a recent article (2022) we proved with L. Zaj\'i\v{c}ek that if $ G\subset\R^n $ is an unbounded open convex set that does not contain a translation of a convex cone with non-empty interior, then there exist $ f:G\to\R $ and a concave…

We show that if $H \leq G$ is a closed amenable and cocompact subgroup of a unimodular locally compact group, then the reduced group C*-algebra of $G$ is not simple. Equivalently, there are unitary representations of $G$ that are weakly…

We consider a convex solid cone $\mathcal{C}\subset\mathbb{R}^{n+1}$ with vertex at the origin and boundary $\partial\mathcal{C}$ smooth away from $0$. Our main result shows that a compact two-sided hypersurface $\Sigma$ immersed in…

We show how to improve on Theorem 10 in [arXiv:0906.4883], describing when subsets in $W^{1,p}(\mathbb{R}^n)$ are totally bounded subsets of $L^q(\mathbb{R}^n)$ for $p<n$ and $p\le q<p^*$. This improvement was first shown by Dosso, Fofana,…

Let $F$ be a non-archimedean local field of characteristic different from $2$ and $G$ be either an odd special orthogonal group ${\rm SO}_{2r+1}(F)$ or a symplectic group ${\rm Sp}_{2r}(F)$. In this paper, we establish the local converse…

We address the problem of existence and uniqueness of a Levi-flat hypersurface $M$ in $C^n$ with prescribed compact boundary $S$ for $n\ge3$. The situation for $n\ge3$ differs sharply from the well studied case $n=2$. We first establish…

The aim of this note is to show that every subset of a given topological space is the intersection of a preopen and a preclosed set, therefore $\beta$-locally closed, and that every topological space is $\beta$-submaximal.

We exhibit an example of covering surface of C*, arising from analytical continuation of a holomorphic germ and failing to be a topological covering, due to singular points and regular ones being projected over the same slits in C*.

We provide necessary and/or sufficient conditions on vector spaces $V$ of real sequences to be a Fr\'{e}chet space such that each coordinate map is continuous, that is, to be a locally convex FK space. In particular, we show that if…

For any Tychonoff space $X$ let $C_p(X)$ (resp., $C^*_p(X)$) be the set of all continuous (resp., and bounded) functions on $X$ with the pointwise convergence topology. Given Tychonoff spaces $X$ and $Y$, Uspenskij \cite{us} proved that if…

Given a convex domain $\Omega\subset \mathbb{R}^{3}$ and an almost-minimizer $E$ of the relative perimeter in $\Omega$, we prove that the closure of $\partial E \cap \Omega$ does not contain vertices of $\Omega$.

In this paper we give sufficient conditions under which a subsemigroup of a topological group is a subgroup, adding to the results given in \cite{Kosh, can, axioms, forum, Hof, cc, locally} where conditions exist (such as locally…

In this paper, we show that the low energy spaces in the prescribed singularity case $\mathcal{E}_{\psi}(X,\theta,\phi)$ have a natural topology which is completely metrizable. This topology is stronger than convergence in capacity.

The main result is that, for any projective compact analytic subset A of dimension q>0 in a reduced complex space X, there is a neighborhood U of A such that, for any covering space Z of X in which the lifting B of A has no noncompact…

We define $\Delta$-Baire spaces. If a paratopological group $G$ is $\Delta$-Baire space, then $G$ is a topological group. Locally pseudocompact spaces, Baire $p$-spaces, Baire $\Sigma$-spaces, products of \v{C}ech-complete spaces are…