Related papers: Order isomorphisms on function spaces

We prove a compact embedding theorem in a class of spaces of piecewise H1 functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the…

In this paper, we prove the following version of the famous Bernstein's theorem: Let $X\subset \mathbb R^{n+k}$ be a closed and connected set with Hausdorff dimension $n$. Assume that $X$ satisfies the monotonicity formula at $p\in X$.…

We study functions on topometric spaces which are both (metrically) Lipschitz and (topologically) continuous, using them in contexts where, in classical topology, ordinary continuous functions are used. We study the relations of such…

In this paper we investigate the relationship between the properties of a compact set $\sigma \subseteq \mathbb{C}$ and the structure of the space $BV(\sigma)$ of functions of bounded variation (in the sense of Ashton and Doust) defined on…

Let \(X\) be a compact metric space and \(E\) be a Banach space. \(\lip (X, E)\) denotes the Banach space of all \(E\)-valued little Lipschitz functions on \(X\). We show that \(\lip (X, E)^{**}\) is isometrically isomorphic to Banach space…

Let $X$ be a completely regular space. For a non-vanishing self-adjoint Banach subalgebra $H$ of $C_B(X)$ which has local units we construct the spectrum $\mathfrak{sp}(H)$ of $H$ as an open subspace of the Stone-Cech compactification of…

We extend to binary relational systems the notion of compact and normal structure, introduced by J.P.Penot for metric spaces, and we prove that for the involutive and reflexive ones, every commuting family of relational homomorphisms has a…

In his paper [Concrete representation of abstract $(M)$-spaces. (A characterization of the space of continuous functions.), Ann. of Math., $42 (2)$ ($1941$), $994$--$1024$.], S. Kakutani gave an interesting representation of the closed…

This paper investigates topological reconstruction, related to the reconstruction conjecture in graph theory. We ask whether the homeomorphism types of subspaces of a space $X$ which are obtained by deleting singletons determine $X$…

We discuss three problems of Koszmider on the structure of the spaces of continuous functions on the Stone compact $K_{\mathcal A}$ generated by an almost disjoint family $\mathcal A$ of infinite subsets of $\omega$ -- we present a solution…

We determine the boundedness and compactness of a large class of operators, mapping from general Banach spaces of holomorphic functions into a particular type of spaces of functions determined by the growth of the functions, or the growth…

Browder (1960) proved that for every continuous function $F : X \times Y \to Y$, where $X$ is the unit interval and $Y$ is a nonempty, convex, and compact subset of $\dR^n$, the set of fixed points of $F$, defined by $C_F := \{ (x,y) \in X…

It was proved by Argyros and Dodos that, for many classes $ C $ of separable Banach spaces which share some property $ P $, there exists an isomorphically universal space that satisfies $ P $ as well. We introduce a variant of their…

Using classical results of infinite-dimensional geometry, we show that the isometry group of the Urysohn space, endowed with its usual Polish group topology, is homeomorphic to the separable Hilbert space. The proof is basedon a lemma about…

The main result of the paper is an extension of the Dirichlet problem from (closures of) bounded open domains U to arbitrary compact subsets X of the complex plane, i.e. the closure of the corresponding space of functions which are harmonic…

In this article, we characterize the left symmetric points in $C(K,X)$, where $K$ is a compact Hausdorff space and $X$ is a Banach space. We also provide necessary and sufficient conditions for the right symmetric points in $C(K,X)$.…

For certain families of compact subsets of the plane, the isomorphism class of the algebra of absolutely continuous functions on a set is completely determined by the homeomorphism class of the set. This is analogous to the…

We show that for smooth manifolds X and Y, any isomorphism between the special algebra of Colombeau generalized functions on X, resp. Y is given by composition with a unique Colombeau generalized function from Y to X. We also identify the…

It is proved that the relation of isomorphism between separable Banach spaces is a complete analytic equivalence relation, i.e., that any analytic equivalence relation Borel reduces to it. Thus, separable Banach spaces up to isomorphism…

Let $\Delta$ be a foliation on a topological manifold $X$, $Y$ be the space of leaves, and $p: X \to Y$ be the natural projection. Endow $Y$ with the factor topology with respect to $p$. Then the group $\mathcal{H}(X, \Delta)$ of foliated…