Related papers: On T-locally compact spaces
We examine locally compact normal spaces in models of form PFA(S)[S], in particular characterizing paracompact, countably tight ones as those which include no perfect pre-image of omega_1 and in which all separable closed subspaces are…
The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft…
The notion of hull-kernel topology on a collection of prime filters in a residuated lattice is introduced and investigated. It is observed that any collection of prime filters is a $T_0$ topological space under the hull-kernel and the dual…
Motivated by ill-posed PDEs such as $\mathrm{div} (v) = F$ we study locally convex topologies $\mathcal{T}_{\mathcal{C}}$ on real vector spaces $X$ that are a ``localized'' version of a locally convex topology $\mathcal{T}$ to members of a…
We discuss the problem of finding an analogue of the concept of a topological space in supergeometry, motivated by a search for a procedure to compactify a supermanifold along odd coordinates. In particular, we examine the topologies…
We will discuss in this paper homogeneous locally conformally Keahler (or shortly homogeneous l.c.K.) manifolds and locally homogeneous l.c.K. manifolds from various aspects of study in the field of l.c.K. geometry. We will provide a survey…
We study the topological structure and the topological dynamics of groups of homeomorphisms of scattered spaces. For a large class of them (including the homeomorphism group of any ordinal space or of any locally compact scattered space),…
We study the properties of topological spaces $(X,\tau)$, where $X$ is a definable set in an o-minimal structure and the topology $\tau$ on $X$ has a basis that is (uniformly) definable. Examples of such spaces include the canonical…
In this paper we introduce and study the local version of the Menger property, namely locally Menger property (or, locally Menger space). We explore some preservation like properties in this space. We also discuss certain situations where…
In the beginning of the 20th century, A. N. Whitehead and T. de Laguna proposed a new theory of space, known as {\em region-based theory of space}. They did not present their ideas in a detailed mathematical form. In 1997, P. Roeper has…
In this paper we introduce and study so-called $k^*$-metrizable spaces forming a new class of generalized metric spaces, and display various applications of such spaces in topological algebra, functional analysis, and measure theory. By…
In this paper, we introduce a Grothendieck topology on the category of totally bounded metric spaces and develop a theory of stacks with respect to this topology. We further define the fine moduli stack of compact metric spaces and prove…
In this paper we will continue the study of p-closed spaces. This class of spaces is strictly placed between the class of strongly compact spaces and the class of quasi-H-closed spaces. We will provide new characterizations of p-closed…
We investigate the mapping class groups of a class of non-Hausdorff topological spaces which includes finite spaces. We show that the mapping class group of a finite space is isomorphic to the homeomorphism group of its $T_0$ quotient. As a…
Two non-discrete Hausdorff group topologies $\tau, \delta$ on a group $G$ are called {\it transversal} if the least upper bound $\tau\vee \delta$ of $\tau$ and $\delta$ is the discrete topology. In this paper, we discuss the existence of…
We study abstract group actions of locally compact Hausdorff groups on CAT(0) spaces. Under mild assumptions on the action we show that it is continuous or has a global fixed point. This mirrors results by Dudley and Morris-Nickolas for…
The dissipated spaces form a class of compacta which contains both the scattered compacta and the compact LOTSes (linearly ordered topological spaces), and a number of theorems true for these latter two classes are true more generally for…
Topological measures and quasi-linear functionals generalize measures and linear functionals. We define and study deficient topological measures on locally compact spaces. A deficient topological measure on a locally compact space is a set…
We characterize those compact Hausdorff spaces K such that the proyective tensor product of C(K) by itself has the Dunford-Pettis Property, answering thus in the negative a question posed by Castillo and Gonzalez.
We prove that every infinite-dimensional (locally convex) linear topological space that can be expressed as a direct limit of finite-dimensional metrizable compacta is (linearly) homeomorphic to the space $R^\infty=\dlim R^n$.