Related papers: A separable non-remainder of H
This paper presents a sufficient condition for a continuum in $R^n$ to be embeddable in $R^n$ in such a way that its image is not an attractor of any iterated function system. An example of a continuum in $R^2$ that is not an attractor of…
We give a new proof of rationality of stable commutator length (scl) of certain elements in surface groups: those represented by curves that do not fill the surface. Such elements always admit extremal surfaces for scl. These results also…
K. Kuperberg found a locally connected, finite-dimensional continuum which is homogeneous but not bihomogeneous. We give a similar but simpler example. Like previous constructions, the example is locally a Cartesian product of Menger…
We show that if $X$ is a compact nonpositively curved cube complex which is a non-product, then $\pi_1 X$ has a proper quotient that is $\pi_1$ of a cube complex with these same properties.
We show the existence of a continuum of Hamiltonian structures for the two-dimensional isotropic harmonic oscillator. In particular, a continuum of Hamiltonian structures having noncommutative coordinates is presented. A study of the…
We prove that if there is a real-valued measurable cardinal then the splitting number is $\aleph_1$. Likewise, if the continuum is real-valued measurable then the reaping number equals the continuum.
We prove that there exist finitely generated, stably finite algebras which are non linear sofic. This was left open by Arzhantseva and P\u{a}unescu in 2017.
Finding separable certificates of stability is important for tractability of analysis methods for large-scale networked systems. In this paper we consider the question of when a nonlinear system which is contracting, i.e. all solutions are…
A topological space $X$ is said to be {\em $Y$-rigid} if any continuous map $f:X\rightarrow Y$ is constant. In this paper we construct a number of examples of regular countably compact $\mathbb R$-rigid spaces with additional properties…
For each vector $x\in \ell^{\infty}$, we can define the non-empty compact set $L_x$ of accumulation points of $x$. Given an infinite subset $A$ of $\mathbb{N}\backslash\{1\}$, we can therefore investigate under which conditions on $A$, the…
We review results concerning homogeneous compacta and discuss some open questions. It is established that indecomposable continua are Alexandroff (resp., Mazurkiewicz, or strong Cantor) manifolds with respect to the class of all continua.…
A projectability result is proved for surfaces of prescribed mean curvature (shortly called $H$-surfaces) spanned in a partially free boundary configuration. Hereby, the $H$-surface is allowed to meet the support surface along its free…
We show that it is consistent that for some uncountable cardinal k, all compactifications of the countable discrete space with remainders homeomorphic to $D^k$ are homeomorphic to each other. On the other hand, there are $2^c$ pairwise…
In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the…
Let k be a field, Q a quiver with countably many vertices and I an ideal of kQ such that kQ/I has finite dimensional Hom-spaces. In this note, we prove that there is no almost split sequence ending at an indecomposable not finitely…
We show that the continua I_u and H* are non-chainable and have span nonzero. Under CH this can be strengthened to surjective symmetric span nonzero. We discuss the logical consequences of this.
We characterize order preserving continuous surjections between compact linearly ordered spaces which admit an averaging operator, together with estimates of the norm of such an operator. This result is used to the study of strengthenings…
We study the existence of non-separable compact spaces that support a measure and are small from the topological point of view. In particular, we show that under Martin's axiom there is a non-separable compact space supporting a measure…
We show (in ZFC) that the cardinality of a compact homogeneous space of countable tightness is no more than the size of the continuum.
We show that there is a compact topological space carrying a measure which is not a weak* limit of finitely supported measures but is in the sequential closure of the set of such measures. We construct compact spaces with measures of…