Related papers: An equivalent condition for a uniform space to be …
Let E be a rank two vector bundle on a scheme X. The following three structures are shown to be equivalent : a) A primitive quadratic map q: E --> L, with values in an invertible module L. b) A double covering f: Y --> X endowed with an…
We give a short proof that, for nice $X$, the based fundamental groupoid of $X$ with topology induced by the compact open topology on the space of paths, is indeed the universal covering space of $X$.
We show that if an open cover of a finite dimensional space is equivariant with respect to some finite group action on the space then there is an equivariant refinement of bounded dimension. This will generalize some constructions of…
Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic…
A family of mappings is called uniformly light if the image of the continuum under these mappings cannot be contracted to a point under the sequence of mappings of the family. In this paper, we are interested in the problem of the uniform…
We consider sufficient conditions which guarantee that a planar embedding has a unique fixed point. We study sufficient conditions which imply the appearing of a globally attracting fixed point for such an embedding.
Let $L^0$ be the vector space of all (equivalence classes of) real-valued random variables built over a probability space $(\Omega, \mathcal{F}, P)$, equipped with a metric topology compatible with convergence in probability. In this work,…
Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point…
We give conditions in order to approximate locally uniformly holomorphic covering mappings of the unit ball of $\mathbb{C}^n$ with respect to an arbitrary norm, with entire holomorphic covering mappings. The results rely on a generalization…
The uniform boundary condition in a normed chain complex asks for a uniform linear bound on fillings of null-homologous cycles. For the $\ell^1$-norm on the singular chain complex, Matsumoto and Morita established a characterisation of the…
We define the compact universal cover of a compact, metrizable connected space (i.e. a continuum) X to be the inverse limit of all continua that regularly cover X. We show that such covers do indeed form an inverse system with bonding maps…
We present necessary and sufficient conditions for an n\times n complex matrix B to be unitarily similar to a fixed unicellular (i.e., indecomposable by similarity) n\times n complex matrix A
We give a sufficient condition for isometric actions to have the congruency of orbits, that is, all orbits are isometrically congruent to each other. As applications, we give simple and unified proofs for some known congruence results, and…
In this note, we prove that every open primary basic semialgebraic set is stably equivalent to the realization space of an even-dimensional neighborly polytope. This in particular provides the final step for Mn\"ev's proof of the…
In this paper, plane polynomial systems having a singular point attracting all orbits in positive time are classified up to topological equivalence. This is done by assigning a combinatorial invariant to the system (a so-called "feasible…
Building on the recent notion of non-uniform complete observability, and on the fact that this property ensures non-uniform exponential detectability, this paper establishes the converse implication under suitable additional assumptions.…
A uniform space is a topological space together with some additional structure which allows one to make sense of uniform properties such as completeness or uniform convergence. Motivated by previous work of J. Rivera-Letelier, we give a new…
The aim of this paper is to investigate the equivalence conditions for uniform perfectness of quasi-metric spaces. We also obtain the invariant property of uniform perfectness under quasim\"obius maps in quasi-metric spaces. In the end, two…
Three themes of general topology: quotient spaces; absolute retracts; and inverse limits - are reapproached here in the setting of metrizable uniform spaces, with an eye to applications in geometric and algebraic topology. The results…
In this paper we give necessary and sufficient conditions for a connection in a plane bundle above a surface to be locally metric. These conditions are easy to be verified in any local chart. Also as a global result we give a necessary…