Related papers: A Core Decomposition of Compact Sets in the Plane

Some new classes of compacta $K$ are considered for which $C(K)$ endowed with the pointwise topology has a countable cover by sets of small local norm--diameter.

A finite relational structure A is called compact if for any infinite relational structure B of the same type, the existence of a homomorphism from B to A is equivalent to the existence of homomorphisms from all finite substructures of B to…

We study fine structural properties related to the interior regularity of $m$-dimensional area minimizing currents mod$(q)$ in arbitrary codimension. We show: (i) the set of points where at least one tangent cone is translation invariant…

A locally conformally product (LCP) structure on compact manifold $M$ is a conformal structure $c$ together with a closed, non-exact and non-flat Weyl connection $D$ with reducible holonomy. Equivalently, an LCP structure on $M$ is defined…

Fix $n\ge3$. For the pure field $K_a=\mathbb Q(\theta)$ with $\theta^n=a$, where $a\neq \pm 1$ is $n$th-power-free, we encode an integral basis in the fixed coordinate $\{1,\theta,\dots,\theta^{n-1}\}$ by its \emph{shape}. We prove a sharp…

Let $\&$ be a continuous triangular norm on the unit interval $[0,1]$ and $\mathbf{A}$ be a cartesian closed and stable subconstruct of the category consisting of all real-enriched categories. Firstly, it is shown that the category…

Generalizing the result of Agronsky and Ceder (1991), we prove that every Peano continuum admits a continuous transformation that is exact Devaney chaotic; that is, it has a dense set of periodic points, and every nonempty open set covers…

We develop a generalized covering space theory for a class of uniform spaces called coverable spaces. Coverable spaces include all geodesic metric spaces, connected and locally pathwise connected compact topological spaces, in particular…

A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreasing. By Hahn-Banach theorem, a positive strong submeasure is…

A compact Hausdorff space X is called a CO space, if every closed subset of X is homeomorphic to an open subset of X. Every successor ordinal with its order topology is a CO space. We find an explicit characterization of the class K of CO…

Let $ G $ be a real simple linear connected Lie group of real rank one. Then, $ X := G/K $ is a Riemannian symmetric space with strictly negative sectional curvature. By the classification of these spaces, $X$ is a real/complex/quaternionic…

We examine space-filling curves, which are surjective continuous maps from $[0,1]$ to some higher-dimensional space, usually the unit square $[0,1]^2$. In particular, we define Peano's curve and Lebesgue's curve, and state some of their…

A \emph{strong coreset} for the mean queries of a set $P$ in ${\mathbb{R}}^d$ is a small weighted subset $C\subseteq P$, which provably approximates its sum of squared distances to any center (point) $x\in {\mathbb{R}}^d$. A \emph{weak…

In 1920s R. L. Moore introduced \emph{upper semicontinuous} and \emph{lower semicontinuous} decompositions in studying decomposition spaces. Upper semicontinuous decompositions were studied very well by himself and later by R.H. Bing in…

A topology on a set $X$ is the same as a projection (i.e. an idempotent linear operator) $cl:2^X\to 2^X$ satisfying $A\subset cl(A)$ for all $A\subset X$. That's a good way to summarize Kuratowski's closure operator. Basic geometry on a set…

Denote by $M(P)$ the configuration space of a planar polygonal linkage, that is, the space of all possible planar configurations modulo congruences, including configurations with self-intersections. A particular interest attracts its subset…

Let M be a matrix whose entries are power series in several variables and determinant det(M) does not vanish identically. The equation det(M)=0 defines a hypersurface singularity and the (co)-kernel of M is a maximally Cohen-Macaulay module…

We generalize a recent result of Clausen: For a number field with integers O, we compute the K-theory of locally compact O-modules. For the rational integers this recovers Clausen's result as a special case. Our method of proof is quite…

We prove that if K is a remainder of the Hilbert space (i.e., K is the complement of the Hilbert space in its metrizable compactification) then every non-one-point closed image of K either contains a compact set with no transfinite…

We consider a coamenable compact quantum group $\mathbb{G}$ as a compact quantum metric space if its function algebra $\mathrm{C}(\mathbb{G})$ is equipped with a Lip-norm. By using a projection $P$ onto direct summands of the Peter--Weyl…