Related papers: An equivalent condition for a uniform space to be …

Let $k$ be any field and $k^s$ its separable closure. Let $X$ be an affine variety over $k$ which is isomorphic to affine $n$-space over the field extension $k^s$. Then $X$ is isomorphic to affine $n$ space over $k$.

The problem when the order polytope and the chain polytope of a finite partially ordered set are unimodularly equivalent will be solved.

Let A={a_s(mod n_s)}_{s=1}^k and B={b_t(mod m_t)}_{t=1}^l be two systems of residue classes. If |{1\le s\le k: x=a_s (mod n_s)}| and |{1\le t\le l: x=b_t (mod m_t)}| are equal for all integers x, then A and B are said to be covering…

In this note we extend a theorem from [13] about uniform circle random coverings

In the present paper we give conclusive arguments pointing at physical equivalence among conformally related metrics. Based on the argument that any consistent effective theory of spacetime must be invariant under the one-parameter group of…

We prove that for a chainable continuum $X$ and every non-zigzag $x\in X$ there exists a planar embedding $\phi:X\to \phi(X)\subset\mathbb R^2$ such that $\phi(x)$ is accessible, partially answering the question of Nadler and Quinn from…

We study the space of stability conditions on the total space of the canonical bundle over the projective plane. We explicitly describe a chamber of geometric stability conditions, and show that its translates via autoequivalences cover a…

This article is concerned with measure equivalence and uniform measure equivalence of locally compact, second countable groups. We show that two unimodular, locally compact, second countable groups are measure equivalent if and only if they…

A condition for the presence of a "gap" between symmetric spaces sufficient for the inclusion of one of these spaces into the other to be disjointly strictly singular is found. This condition is stated in terms of fundamental functions of…

We continue the work of [1, 2, 3] by analyzing the equivalence relation of bi-embeddability on various classes of countable planes, most notably the class of countable non-Desarguesian projective planes. We use constructions of the second…

This article describes a structure that metric spaces can be equipped with so that they resemble normed vector spaces and examines necessary and sufficient conditions for the existence of such a structure on a general metric space.

Necessary and sufficient conditions for a Riemannian product to be conformally equivalent to an Einstein manifold are given. Such spaces which are complete are characterized.

We study trace theoretic concurrent systems. This setting encompasses safe (1-bounded) Petri nets. We introduce a notion of irreducible concurrent system and we prove the equivalence between irreducibility and a "spectral property". The…

Assume hat a functionally Hausdorff space $X$ is a continuous image of a \v{C}ech complete space $P$ with Lindel\"of number $l(P)<\mathfrak c$. Then the following conditions are equivalent: (i) every compact subset of $X$ is scattered, (ii)…

Making use of the method of subordination chains, we obtain some sufficient conditions for the univalence of an integral operator. In particular, as special cases, our results imply certain known univalence criteria. A refinement to a…

The uniform structure on a differential space defined by a family of generators is considered.

Brodskiy, Dydak, LaBuz, and Mitra introduced the concepts of uniform joinability and local uniform joinability for uniform spaces when developing their theory of generalized uniform covering maps which was motivated by a paper by…

We prove realizability theorems for vector-valued polynomial mappings, real-algebraic sets and compact smooth manifolds by moduli spaces of planar linkages. We also establish a relation between universality theorems for moduli spaces of…

In a polar space, embeddable into a projective space, we fix a subspace, that is contained in some hyperplane. The complement of that subspace resembles a slit space or a semiaffine space. We prove that under some assumptions the ambient…

The idea behind universal coating is to have a thin layer of a specific substance covering an object of any shape so that one can measure a certain condition (like temperature or cracks) at any spot on the surface of the object without…