相关论文: Wallman-Frink proximities
To study a noncompact Riemannian manifold, it is often useful to find a compactification. We discuss several common compactifications and survey some recent results.
We study locally compact convergence groups, in particular the link between the convergence property and the Specker compactifications (a genaralization of the ends) of a group.
In finite graphs, finite-order tangles offer an abstract description of highly connected substructures. In infinite graphs, infinite-order tangles compactify the graphs in the same way the ends compactify connected locally finite graphs.…
Let $X$ be a space. A space $Y$ is called an extension of $X$ if $Y$ contains $X$ as a dense subspace. For an extension $Y$ of $X$ the subspace $Y\backslash X$ of $Y$ is called the remainder of $Y$. Two extensions of $X$ are said to be…
In this paper, we will use investigate the existence of compactifications with particular convergence properties - pseudoradial, radial, sequential and Fr\'echet-Urysohn - through the use of spoke systems.
In this paper we improve and extend some best proximity point results concerning the so-called proximal contractions. Specifically, compactness assumptions under the sets A and B are removed to consider completeness conditions instead.
Generalizing de Vries Compactification Theorem and strengthening Leader Local Compactification Theorem, we describe the partially ordered set $(\LL(X),\le)$ of all (up to equivalence) locally compact Hausdorff extensions of a Tychonoff…
In this informal expository note, we quickly introduce and survey compactifications of strata of holomorphic 1-forms on Riemann surfaces, i.e. spaces of translation surfaces. In the last decade, several of these have been constructed,…
In this article, we investigate for some sufficient conditions for the existence and uniqueness of best proximity points for the topological $p$-proximal contractions and $p$-proximal contractive mappings on arbitrary topological spaces.…
We present some recent results in Fibrewise General Topology with special regard to the theory of Tychonoff compactifications of mappings. Several open problems are also proposed.
In this note, we reformulate Donaldson's construction as a compactness result. Approximately holomorphic sections accumulate to "limit holomorphic sections" and uniform transversality properties of the approximately holomorphic sections…
This paper studies compactifications of moduli spaces involving closed Riemann surfaces. The first main result identifies the homeomorphism types of these compactifications. The second main result introduces orbicell decompositions on these…
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…
This paper studies coarse compactifications and their boundary. We introduce two alternative descriptions to Roe's original definition of coarse compactification. One approach uses bounded functions on $X$ that can be extended to the…
A space Y is called an extension of a space X if Y contains X as a dense subspace. An extension Y of X is called a one-point extension if Y-X is a singleton. Compact extensions are called compactifications and connected extensions are…
A characterization of $\varkappa$-metrizable compacta in terms of extension of functions and usco retractions into superextensions is established.
We extend the definition of quasi-finite complexes by considering not necessarily countable complexes. We provide a characterization of quasi-finite complexes in terms of L-invertible maps and dimensional properties of compactifications.…
We study the compactification of nonautonomous systems with autonomous limits and related dynamics. Although the $C^{1}$ extension of the compactification was well established, a great number of problems arising in bifurcation and stability…
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.
We introduce the notion of soficity for locally compact groups and list a number of open problems.