Related papers: Some remarks on anti-topological spaces

In this paper, we introduce a novel distance-like notion of furtherness for finite topological spaces, demonstrating that every finite space can be viewed as an asymmetric pseudometric space. In particular, we show that every finite T0…

Vacuum Einstein theory in three spacetime dimensions is locally trivial, but admits many solutions that are globally different, particularly if there is a negative cosmological constant. The classical theory of such locally "anti-de Sitter"…

In this thesis we propose and study a theory of ordered locales, a type of point-free space equipped with a preorder structure on its frame of opens. It is proved that the Stone-type duality between topological spaces and locales lifts to a…

We present old and new characterizations of core spaces, alias worldwide web spaces, originally defined by the existence of supercompact neighborhood bases. The patch spaces of core spaces, obtained by joining the original topology with a…

Finite topological spaces are in bijective correspondence with preorders on finite sets. We undertake their study using combinatorial tools that have been developed to investigate general discrete structures. A particular emphasis will be…

These expository notes are dedicated to the study of the topology of configuration spaces of manifolds. We give detailed computations of many invariants, including the fundamental group of the configuration spaces of $\mathbb{R}^2$, the…

Classes of Banach spaces that are finitely, strongly finitely or elementary equivalent are introduced. On sets of these classes topologies are defined in such a way that sets of defined classes become compact totally disconnected…

We explore the notion of spatial extent and structure, already alluded to in earlier literature, within the formulation of quantum mechanics on the noncommutative plane. Introducing the notion of average position and its measurement, we…

Closure spaces are a generalisation of topological spaces obtained by removing the idempotence requirement on the closure operator. We adapt the standard notion of bisimilarity for topological models, namely Topo-bisimilarity, to closure…

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),…

This review aims to cover the central aspects of current research in cosmic topology from a topological and observational perspective. Beginning with an overview of the basic concepts of cosmology, it is observed that though a determinant…

The aim of this short note is to develop a (co)homology theory for topological spaces together with the specialisation preorder. A known way to construct such a (co)homology is to define a partial order on the topological space starting…

This is a survey of topological properties of open, complete nonpositively curved manifolds which may have infinite volume. Topics include topology of ends, restrictions on the fundamental group, as well as a review of known examples.

Non-orientable nanostructures are becoming feasable today. This lead us to the study of spin in these geometries. Hence a physically sound definition of spin is suggested. Using our definition, we study the question of the number of…

In this note we review some aspects of topological censorship. We present several (actually five) alternative sets of hypotheses which allow the proof of a topological censorship theorem for spacetimes with conformal completions at infinity…

In this paper we introduce the concept of the rectangular metric like spaces, along with its topology and we prove some fixed point theorems under different contraction principles. We introduce the concept of modified metric-like space as…

We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.

The goal of the paper is to set the foundations and prove some topological results about moduli spaces of non-smooth metric measure structures with non-negative Ricci curvature in a synthetic sense (via optimal transport) on a compact…

The concept of cone metric spaces with $w-$distance was introduced by H. Lakzian and F. Arabyani [16] in $2009.$ In $2020,$ Branga and Olaru [4] put forth the idea of cone metric spaces over topological module. In this paper, we compose…

The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…