Related papers: Sober topologies on a set
We study topologization of the semigroup $\mathscr{O\!\!I}\!_n(L)$ of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set $(L,\leqslant)$. In particular we show that every $T_1$ left-topological…
We construct and characterize tight binding Hamiltonians which contain a completely flat topological band made of continuum lowest Landau level wavefunctions sampled on a lattice. We find an infinite family of such Hamiltonians, with simple…
We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…
We define a notion of {\it positive part} of a lattice $\Lambda$ and we endow the set of such positive parts with a topology. We then study some properties of this topology, by comparing it with the one of $V^*/\RM_{> 0}$, where $V^*$ is…
We show that the homeomorphism group of a surface without boundary does not admit a Hausdorff group topology strictly coarser than the compact-open topology. In combination with known automatic continuity results, this implies that the…
Given an arbitrary spectral space $X$, we endow it with its specialization order $\leq$ and we study the interplay between suprema of subsets of $(X,\leq)$ and the constructible topology. More precisely, we investigate about when the…
In this paper, we mainly study the function spaces related to H-sober spaces. For an irreducible subset system H and $T_{0}$ spaces $X$ and $Y$, it is proved that $Y$ is H-sober iff the function space $\mathbb{C}(X, Y)$ of all continuous…
The density topology $\cal T$ is a topology on the real line, finer than the usual topology, having as its open sets the measurable subsets of ${\mathbb R}$, which are of density 1 at each of their points. The aim of this paper is to…
A topological space $X$ is called submaximal if every dense subset of $X$ is open. In this paper, we show that if $\beta X$, the Stone-\v{C}ech compactification of $X$, is a submaximal space, then $X$ is a compact space and hence $\beta…
The notion of sobriety is extended to the realm of topological spaces valued in a commutative and unital quantale, via an adjunction between a category of quantale modules and the category of quantale-valued topological spaces. Relations…
In this paper we study topological properties of stable Hamiltonian structures. In particular, we prove the following results in dimension three: The space of stable Hamiltonian structures modulo homotopy is discrete; there exist stable…
In this paper, we provide a uniform approach to $d$-spaces, sober spaces and well-filtered spaces, and develop a general framework for dealing with all these spaces. For a subset system H, the theory of H-sober spaces and super H-sober…
The concepts of topology have a profound impact on physics research spanning the fields of condensed matter, photonics and acoustics and predicting topological states that provide unprecedented versatility in routing and control of waves of…
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…
We provide the set of filters (saturated submonoids) in a commutative monoid with a topology (like the spectrum of a ring) and study the resulting spaces.
While topology given by a linear order has been extensively studied, this cannot be said about the case when the order is given only locally. The aim of this paper is to fill this gap. We consider relation between local orderability and…
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…
This paper deals with the notion of weak Lawvere-Tierney topology on a topos. Our motivation to study such a notion is based on the observation that the composition of two Lawvere-Tierney topologies is no longer idempotent, when seen as a…
We present several equivalent conditions of the continuity of the supremum function from the square of the Scott space of $C(X)$ to itself under mild assumptions, where $C(X)$ denotes the lattice of closed subsets of a $\mathbf{T_0}$…
M. Escard\'o et al. asked whether the core compactly generated topology of a sober space is again sober and the sobrification of a core compactly generated space again core compactly generated. In this note, we answer the problem by…