Related papers: Sober topological spaces valued in a quantale
For each commutative and integral quantale, making use of the fuzzy order between closed sets, a theory of sobriety for quantale-valued cotopological spaces is established based on irreducible closed sets.
As a natural extension of the ongoing development of a theory of ideals in commutative quantales with an identity element, this article aims to study into the analysis of certain topological properties exhibited by distinguished classes of…
We define a class of subsets of a topological space that coincides with the class of compact saturated subsets when the space is sober, and with enough good properties when the space is not sober. This class is introduced especially in view…
In this paper we study some frames associated to an $R$-module $M$. We define semiprimitive submodules and we prove that they form an spatial frame canonically isomorphic to the topology of $Max(M)$. We characterize the soberness of…
In this paper we characterize the projective modules over an arbitrary quantale, and then we apply such a characterization in order to define the K_0 group of a quantale. Then we study congruences of quantales and quantale modules by means…
In this paper, we provide a comprehensive analysis of involutive quantales, with a particular focus on quantic frames. We extend the axiomatic foundations of quantale-enriched topological spaces to include closure under the anti-homomorphic…
We observe that the category of topological space, uniform spaces, and simplicial sets are all, in a natural way, full subcategories of the same larger category, namely the simplicial category of filters; this is, moreover, implicit in the…
We characterize the convergence spaces $(X,\xi)$ such that the space of points of $(\mathbb{P}X,\lim_{\xi})$ in the category of convergence lattices is $(X,\xi)$. On the way, we study variants of sobriety and of the axiom $T_{D}$ in…
This paper presents a study of separation axioms and sobriety of bitopological spaces from the point of view of fuzzy topology via identifying bitopological spaces with topological spaces valued in the Boolean algebra of four elements. A…
We study the set of localizations of an integral domain from a topological point of view, showing that it is always a spectral space and characterizing when it is a proconstructible subspace of the space of all overrings. We then study the…
Several variations on the definition of a Formal Topology exist in the literature. They differ on how they express convergence, the formal property corresponding to the fact that open subsets are closed under finite intersections. We…
There are two rather distinct approaches to Morse theory nowadays: smooth and discrete. We propose to study a real valued function by assembling all associated sections in a topological category. From this point of view, Reeb functions on…
In this paper, we examine the notion of topological stability and its relation to the shadowing properties in zero-dimensional spaces. Several counter-examples on the topological stability and the shadowing properties are given. Also, we…
The soft topological spaces and some their related concepts have stud- ied in [7]. In this paper, we introduce and study the notions of soft connected topological spaces after a review of preliminary definitions.
The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the…
Given an affine algebraic variety V and a quantization A of its coordinate ring, it is conjectured that the primitive ideal space of A can be expressed as a topological quotient of V. Evidence in favor of this conjecture is discussed, and…
Based on topological Rudin's Lemma, we investigate two new kinds of sets - Rudin sets and well-filtered determined sets in $T_0$ topological spaces. Using such sets, we formulate and prove some new characterizations for well-filtered spaces…
We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…
A class of Cantor-type spaces and related geometric structures are discussed.
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…