Related papers: Order preserving quotient lifting properties

We characterize order preserving continuous surjections between compact linearly ordered spaces which admit an averaging operator, together with estimates of the norm of such an operator. This result is used to the study of strengthenings…

A function $f:X\to Y$ between topological spaces is called {\em compact-preserving} if the image $f(K)$ of each compact subset $K\subset X$ is compact. We prove that a function $f:X\to Y$ defined on a strong Frechet space $X$ is…

Various problems on integers lead to the class of congruence preserving functions on rings, i.e. functions verifying $a-b$ divides $f(a)-f(b)$ for all $a,b$. We characterized these classes of functions in terms of sums of rational…

We characterize inclusions of compact noncommutative convex sets with the property that every continuous affine function on the smaller set can be extended to a continuous affine function on the larger set with a uniform bound. As an…

We obtain a lifting property for finite quotients of algebraic groups, and applications to the structure of these groups.

We contribute to the theory for minimal liftings of cut-generating functions. In particular, we give three operations that preserve the so-called covering property of certain structured cut-generating functions. This has the consequence of…

This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…

This paper considers homogeneous order preserving continuous maps on the normal cone of an ordered normed vector space. It is shown that certain operators of that kind which are not necessarily compact themselves but have a compact power…

This paper aims to establish the theoretical foundation for shift inclusion in mathematical morphology. In this paper, we prove that the morphological opening and closing concerning structuring elements of shift inclusion property would…

Let $f$ be a holomorphic mapping between compact complex manifolds. We give a criterion for $f$ to have {\it unobstructed deformations}, i.e. for the local moduli space of $f$ to be smooth: this says, roughly speaking, that the group of…

Lifting properties for Banach spaces are studied. An alternate version of the lifting property due to Lindenstrass and Tzafriri is proposed and a characterization, up to isomorphism, is given. The quotient lifting property for pairs of…

Any compact surface supports a continuous action of the orientation preserving affine group of the real line which is fixed point free (Lima and Plante). It is generally admitted that this action can be taken smooth although it is not easy…

A method of proving local continuity of concave functions on convex set possessing the $\mu$-compactness property is presented. This method is based on a special approximation of these functions. The class of $\mu$-compact sets can be…

Let $\varphi\colon X\to Y$ be an affine continuous surjection between compact convex sets. Suppose that the canonical copy of the space of real-valued affine continuous functions on $Y$ in the space of real-valued affine continuous…

We introduce the notion centre of a convex set and study the space of continuous affine functions on a compact convex set with a centre. We show that these spaces are precisely the dual of a base normed space in which the underlying base…

We prove the Cartan and Choquet properties for the fine topology on a complete metric space equipped with a doubling measure supporting a $p$-Poincar\'e inequality, $1 < p< \infty$. We apply these key tools to establish a fine version of…

The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space,…

In the paper we proved that for a compact $X$ inclusion $I_{f}(X)\in ANR$ holds if and only if $X\in ANR$. Further, it is shown that the functor $I_{f}$ preserves property of a compact to be $Q$-manyfold or a Hilbert cube, preserves…

We establish a dilation-theoretic characterization of the Choquet order on the space of measures on a compact convex set using ideas from the theory of operator algebras. This yields an extension of Cartier's dilation theorem to the…

We define lifting properties for universal algebras, which we study in this general context and then particularize to various such properties in certain classes of algebras. Next we focus on residuated lattices, in which we investigate…