Related papers: A locally connected continuum without convergent s…

We construct examples of non-bi-orderable one-relator groups without generalized torsion. This answers a question asked in [2].

We present a connected version of the compact $L$-space constructed by Kenneth Kunen under CH. We show that this provides a Corson compact space $K$ such that the Banach space $C(K)$ is isomorphic to no space of continuous function on a…

We prove the existence of a 2-dimensional nonaspherical simply connected cell-like Peano continuum (the space itself was constructed in one of our earlier papers). We also indicate some relations between this space and the well-known…

We develop a formalism relating nonlocal current continuity to spatial symmetries of subparts in discrete Schr\"odinger systems. Breaking of such local symmetries hereby generates sources or sinks for the associated nonlocal currents. The…

We show that a complemented subspace of a locally convex direct sum of an uncountable collection of Banach spaces is a locally convex direct sum of complemented subspaces of countable subsums. As a corollary we prove that a complemented…

In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of…

This paper deals with a singular nonlocal phase field system of conserved type.Colli--K.\ [Nonlinear Anal.\ 190 (2020)] have derived existence of solutions to a singular phase field system of conserved type. On the other hand,…

We construct projections from the space of differential k-forms which belong to L2 and whose exterior derivative also belongs to L2, to finite dimensional subspaces of piecewise polynomial differential forms defined on a simplicial mesh.…

We show that the endpoint set of a Suslinian chainable continuum must be zero-dimensional at some point. In particular, it cannot be homeomorphic to complete Erd\H{o}s space. This answers a question of Jerzy Krzempek.

In this paper we continue the analysis undertaken in a series of previous papers on structures arising as completions of C*-algebras under topologies coarser that their norm and we focus our attention on the so-called {\em locally convex…

We present a spectral sequence connecting the continuous and 'locally continuous' group cohomologies for topological groups. As an application it is shown that for contractible topological groups these cohomology concepts coincide. Similar…

Let $(\Gamma,\mathbb{P})$ be a relatively hyperbolic group pair that is relatively one ended. Then the Bowditch boundary of $(\Gamma,\mathbb{P})$ is locally connected. Bowditch previously established this conclusion under the additional…

We show that the classical example $X$ of a 3-dimensional generalized manifold constructed by van Kampen is another example of not homologically locally connected (i.e. not HLC) space. This space $X$ is not locally homeomorphic to any of…

We construct an indecomposable continuum with exactly one strong non-cut point. The method is an adaptation of Bellamy $[1]$. We start with an $\omega_1$-chain of indecomposable metric continua and retractions. The inverse limit is an…

We take a few steps towards constructing a string-inspired nonlocal extension of the Standard Model. We start by illustrating how quantum loop calculations can be performed in nonlocal scalar field theory. In particular, we show the…

We consider the Maxwell-Chern-Simons-Higgs system in Lorenz gauge and use a null condition to show local well-psoedness for low regularity data. This improves a recent result of J. Yuan.

We prove that the existence of Banach spaces with $L$-orthogonal sequences but without $L$-orthogonal elements is independent of the standard foundation of Mathematics, ZFC. This provides a definitive answer to…

The main result of this article is: THEOREM. Every homogeneous locally conical connected separable metric space that is not a $1$-manifold is strongly $n$-homogeneous for each $n \geq 2$ and countable dense homogeneous. Furthermore,…

In this paper, we consider a kind of area preserving non-local flow for convex curves in the plane. We show that the flow exists globally, the length of evolving curve is non-increasing, and the curve converges to a circle in C^{\infty}…

We introduce an idea for generalization of a local cohomology module, which we call a local cohomology module with respect to a pair of ideals (I,J), and study their various properties. Some vanishing and nonvanishing theorems are given for…