Related papers: Embedding Theorems for function spaces

In this paper, we find at the properties of the family lambda which imply that the function space C(X,R^alpha) with the lambda-open topology is a semitopological group (paratopological group, topological group, topological vector space and…

A Tychonoff space $X$ is called $\kappa$-pseudocompact if for every continuous mapping $f$ of $X$ into $\mathbb{R}^\kappa$ the image $f(X)$ is compact. This notion generalizes pseudocompactness and gives a stratification of spaces lying…

Let E be a topological space and F a uniform space. We introduce a new topology (in fact a uniform structure) called the V-congergence on the space of applications from E to F such that C(E,F) is closed for this topology and the restriction…

This paper is devoted to the construction of norm-preserving maps between bounded cohomology groups. For a graph of groups with amenable edge groups we construct an isometric embedding of the direct sum of the bounded cohomology of the…

In this paper, we discuss some questions about compactness in MV-topological spaces. More precisely, we first present a Tychonoff theorem for such a class of fuzzy topological spaces and some consequence of this result, among which, for…

We prove that an $\mathbb{R}$-action on a compact metric space embeds equivariantly in the space of one-Lipschitz functions $\mathbb{R}\to[0,1]$ if its fixed point set can be topologically embedded in the unit interval. This is a refinement…

We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…

We consider classes T of topological spaces (referred to as T-spaces) that are stable under continuous images and frequently under arbitrary products. A local T-space has for each point a neighborhood base consisting of subsets that are…

We prove that, for any topological space $X$ and any metric space $(Y,d)$, the fine topology on the space of continuous functions from $X$ into $Y$ is independent of the metric $d$.

In this paper we have studied the idea of ideal completeness of function spaces Y to the power X with respect to pointwise uniformity and uniformity of uniform convergence. Further involving topological structure on X we have obtained…

We prove a fixed point theorem for closed-graphed, decomposable-valued correspondences whose domain and range is a decomposable set of functions from an atomless measure space to a topological space. One consequence is an improvement of the…

In this paper we establish a direct connection between stable approximate unitary equivalence for $*$-homomorphisms and the topology of the KK-groups which avoids entirely C*-algebra extension theory and does not require nuclearity…

For a Tychonoff space $X$, we denote by $(C(X), \tau_k, \tau_p)$ the bitopological space of all real-valued continuous functions on $X$ where $\tau_k$ is the compact-open topology and $\tau_p$ is the topology of pointwise convergence. In…

We describe the proof that the period map from the Torelli space of Calabi-Yau manifolds to the classifying space of polarized Hodge structures is an embedding. The proof is based on the constructions of holomorphic affine structure on the…

For a Tychonoff space $X$, we denote by $C_p(X)$ the space of all real-valued continuous functions on $X$ with the topology of pointwise convergence. We give the functional characterization of the covering property of Hurewicz.

In this paper we focus on the set-open topologies on the group $\mathcal{H}(X)$ of all self-homeomorphisms of a topological space $X$ which yield continuity of both the group operations, product and inverse function. As a consequence, we…

The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…

Using the idea of strong uniform convergence on bornology, Caserta, Di Maio and Ko\v{c}inac studied open covers and selection principles in the realm of metric spaces (associated with a bornology) and function spaces (w.r.t. the topology of…

For any Tychonoff space $X$ let $C_p(X)$ (resp., $C^*_p(X)$) be the set of all continuous (resp., and bounded) functions on $X$ with the pointwise convergence topology. Given Tychonoff spaces $X$ and $Y$, Uspenskij \cite{us} proved that if…

We prove that for any topological space $X$ of countable tightness, each \sigma-convex subspace $\F$ of the space $SC_p(X)$ of scatteredly continuous real-valued functions on $X$ has network weight $nw(\F)\le nw(X)$. This implies that for a…