Related papers: On the Surjectivity of Certain Maps II: For Genera…

In this article, the projectivity of finitely generated flat modules of a commutative ring are studied from a topological point of view. Then various interesting results are obtained. For instance, it is shown that if a ring has either a…

Let $n$ be a positive integer and $H$ a Hilbert space. The description of the general form of bijective maps on the set of $n$-dimensional subspaces of $H$ preserving the maximal principal angle has been obtained recently. This is a…

We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…

We introduce a new topological generalization of the $\sigma$-projective hierarchy, not limited to Polish spaces. Earlier attempts have replaced $^{\omega}\omega$ by $^{\kappa}\kappa$, for $\kappa$ regular uncountable, or replaced countable…

There exists a homomorphism from the affine super Yangian to the completion of the universal enveloping algebra of $\widehat{\mathfrak{gl}}(m|n)$, called the evaluation map. In this paper, we show that this homomorphism is surjective. Via…

The purpose of this contribution is to give a coherent account of a particular narrative which links locales, geometric theories, sheaf semantics and constructive commutative algebra. We are hoping to convey a firm grasp of three ideas: (1)…

We study the homotopy types of certain spaces closely related to the spaces of algebraic (rational) maps from the $m$ dimensional real projective space into the $n$ dimensional complex projective space for $2\leq m\leq 2n$ (we conjecture…

We consider the problem of the observability of positively expansive maps by the time series associated to continuous real functions. For this purpose we prove a general result on the generic observability of a locally injective map of a…

For a set-valued map, we characterize, in terms of its (unconvexified or convexified) graphical derivatives near the point of interest, positively homogeneous maps that are generalized derivatives in the sense of [20]. This result…

The aim of this paper is to give a proof of the restriction theorems for principal bundles with a reductive algebraic group as structure group in arbitrary characteristic. Let $G$ be a reductive algebraic group over any field $k=\bar{k}$,…

We examine the problem of projecting subsets of a commutative, positively ordered monoid into an $o$-ideal. We prove that to this end one may restrict to a sufficient subset, for whose cardinality we provide an explicit upper bound. Several…

A proof of Grothendieck--Serre conjecture on principal bundles over a semi-local regular ring containing an infinite field is given in [FP] recently. That proof is based significantly on Theorem 1.0.1 stated below in the Introduction and…

Let $R$ be an affine domain of characteristic zero with finite quotients. We prove that a polynomial map over $R$ is surjective if and only if it is surjective over $\hat{R_{\mathfrak{m}}}$, the completion of $R$ with respect to…

Let w: Map(X,Y;f) -> Y denote a general evaluation fibration. Working in the setting of rational homotopy theory via differential graded Lie algebras, we identify the long exact sequence induced on rational homotopy groups by w in terms of…

We prove that the multiplication of sections of globally generated line bundles on a model wonderful variety M of simply connected type is always surjective. This follows by a general argument which works for every wonderful variety and…

We present constructions and bounds for additive codes over a finite field in terms of their geometric counterpart, i.e., projective systems. It is known that the maximum number of $(h-1)$-spaces in PG$(2,q)$, such that no hyperplane…

We consider injectivity and surjectivity of some maps on the exterior algebra of isomorphic finite-dimensional vector spaces. We prove the properties of the maps in full generality, for any dimension of the vector space and any subspace. We…

We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…

We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. In a previous paper we have shown that the inclusion of the first space into the second one is a homotopy…

The main goal of this paper is to give a general method to compute (via computer algebra systems) an explicit set of generators of the ideals of the projective embeddings of some ruled surfaces, namely projective line bundles over curves…