Related papers: Compact pseudoconcave sets
We combine ideas of Scott and Swarup on good position for almost invariant subsets of a group with ideas of Sageev on constructing cubings from such sets. We construct cubings which are more canonical than in Sageev's original construction.…
In this note we consider compact homomorphisms and endomorphisms between various Dales-Davie algebras. In particular, we obtain fairly complete results when the underlying set is the disc or the unit circle. Comparable results when the…
Every symmetric generating functional of a convolution semigroup of states on a locally compact quantum group is shown to admit a dense unital $*$-subalgebra with core-like properties in its domain. On the other hand we prove that every…
This paper presents new results from a detailed study of the structure of autocatalytic sets. We show how autocatalytic sets can be decomposed into smaller autocatalytic subsets, and how these subsets can be identified and classified. We…
Let K be the function field of a connected regular scheme S of dimension 1, and let f : X -> Y be a finite cover of projective smooth and geometrically connected curves over K with g(X) greater or equal to 2. Suppose that f can be extended…
A topological space $X$ is called $\Cal A$-real compact, if every algebra homomorphism from $\Cal A$ to the reals is an evaluation at some point of $X$, where $\Cal A$ is an algebra of continuous functions. Our main interest lies on…
We characterize some variations of pseudoskeleton (also called CUR) decompositions for matrices and tensors over arbitrary fields. These characterizations extend previous results to arbitrary fields and to decompositions which use…
An antinorm is a concave analogue of a norm. In contrast to norms, antinorms are not defined on the entire space $R^d$ but on a cone $K\subset R^d$. They are applied in the matrix analysis, optimal control, and dynamical systems. Their…
We consider the space of real-valued continuously differentiable functions on a compact subset of a euclidean space. We characterize the completeness of this space and prove that the space of restrictions of continuously differentiable…
The aim of this paper is twofold. On one hand the generalized Minkowski sets are defined and characterized. On the other hand, the Motzkin decomposable sets, along with their epigraphic versions are considered and characterized in new ways.…
We present a short complete proof of the existence of the normal cycle of a compact subanalytic set. The approach is inspired by some old ides of Joseph Fu, uses Morse theoretic techniques and $o$-minimal topology.
It is common that a Sobolev space defined on $\mathbb{R}^m$ has a non-compact embedding into an $L^p$-space, but it has subspaces for which this embedding becomes compact. There are three well known cases of such subspaces, the Rellich…
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.
Renormalizations can be considered as building blocks of complex dynamical systems. This phenomenon has been widely studied for iterations of polynomials of one complex variable. Concerning non-polynomial hyperbolic rational maps, a recent…
A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.
We introduce some compact orbifolds on which there is a certain finite group action having a simple convex polytope as the orbit space. We compute the orbifold fundamental group and homology groups of these orbifolds. We calculate the…
We prove some results which give sufficient conditions so that pointwise approximation of negative plurisubharmonic functions on complex varieties by continuous plurisubharmonic ones is possible.
We characterize analytic curves that contain non-trivial self-affine sets. We also prove that compact algebraic surfaces cannot contain non-trivial self-affine sets.
We prove a compactness theorem for pseudopower operations of the form $pp_{\Gamma(\mu,\sigma)}(\mu)$ where $\aleph_0<\sigma=cf(\sigma)\leq cf(\mu)$. Our main tool is a result that has Shelah's cov vs. pp Theorem as a consequence. We also…
A regular separable first-countable countably compact space is called a Nyikos space. In this paper, we give a partial solution to an old problem of Nyikos by showing that each locally compact Nyikos inverse topological semigroup is…