Non-Hausdorff Topology and Domain Theory

DOI10.1017/CBO9781139524438zbMath1280.54002OpenAlexW438549760MaRDI QIDQ4914616

Publication date: 15 April 2013

Full work available at URL: https://doi.org/10.1017/cbo9781139524438

metric spaces completeness domain theory spectral spaces stably compact spaces point-set topology non-Hausdorff topology formal balls Hofmann-Mislove Theorem quasi-metrics Smyth-completeness Yoneda-completeness compact pospaces Choquet-completeness soberness asymmetric metrics

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Fairly general properties of topological spaces (54D99) Research exposition (monographs, survey articles) pertaining to general topology (54-02)

Related Items

KF-CONTINUOUS SPACES AND KF-QUASICONTINUOUS SPACES, Formal balls of Q-categories, On function spaces equipped with Isbell topology and Scott topology, Consistent disjunctive sequent calculi and Scott domains, Distance Domains: Completeness, Continuity as a computational effect, Unnamed Item, A note on coherence of dcpos, Hofmann-Mislove type definitions of non-Hausdorff spaces, A characterisation of weightable quasi-metric generating functions, Infinitary Noetherian constructions I. Infinite words, Unnamed Item, Separating minimal valuations, point-continuous valuations, and continuous valuations, Yoneda completeness and flat completeness of ordered fuzzy sets, On well-filtered spaces and ordered sets, Some new results on six types mappings between L-convex spaces, Unnamed Item, Probability, valuations, hyperspace: Three monads on top and the support as a morphism, Weak well-filtered spaces and coherence, Maximal point spaces of dcpos satisfying the Lawson condition, Local T2 extended pseudo-quasi-semi metric spaces, A new convergence inducing the SI-topology, On two problems about sobriety of topological spaces, Kantorovich-Rubinstein quasi-metrics. I: Spaces of measures and of continuous valuations, The B-topology on \(S^{\ast}\)-doubly quasicontinuous posets, Unnamed Item, Some thoughts on countable Lindelöf products, Sober spaces, Lattice-free and point-free: Vickers duality for subbases of stably locally compact spaces, On \(P\)-sober spaces, On a quotient \(S\)-set induced by countably infinite decreasing chains, T-complete KM-fuzzy metric spaces via domain theory, A compact space is not always \(SI\)-compact, Recursive solution of initial value problems with temporal discretization, Weakly weighted generalised quasi-metric spaces and semilattices, Infinitary Noetherian constructions II. Transfinite words and the regular subword topology, Fixed points and Noetherian topologies, Characterizations of quasi-metric and \(G\)-metric completeness involving \(w\)-distances and fixed points, On some results related to sober spaces, THE WADGE ORDER ON THE SCOTT DOMAIN IS NOT A WELL-QUASI-ORDER, Subordinations on bounded distributive lattices, Topological representations of Lawson compact algebraic L-domains and Scott domains, Descriptive complexity of \(\mathsf{qc} \mathsf{b}_0\)-spaces, Once again on topological spaces containing a dense completely metrizable subset, Prototypes, poles, and tessellations: towards a topological theory of conceptual spaces, A topological duality for dcpos, Unnamed Item, De groot duality for represented spaces, A domain-theoretic framework for robustness analysis of neural networks, Not every countable complete distributive lattice is sober, Scott topology on Smyth power posets, The order-K-ification monads, A construction of free dcpo-cones, Quasicontinuous spaces, Ekeland variational principle and its equivalents in T₁-quasi-uniform spaces, Yoneda completeness, Unnamed Item, On a problem about strictly completely regular ordered spaces posed by Lawson, The categorical equivalence between domains and interpolative generalized closure spaces, A new cardinal function on topological spaces, Kantorovich-Rubinstein quasi-metrics IV: lenses, quasi-lenses and forks, (q1, q2)-quasimetrics bi-Lipschitz equivalent to 1-quasimetrics, Unnamed Item, Unnamed Item, Unnamed Item, Clarke's generalized gradient and Edalat's L-derivative, The Reverse Mathematics of wqos and bqos, Formal balls in fuzzy quasi-metric spaces, A complete Heyting algebra whose Scott space is non-sober, On Fixed Point Theory in Partially Ordered (Quasi-)metric Spaces and an Application to Complexity Analysis of Algorithms, Products and projective limits of continuous valuations on T₀ spaces, Unnamed Item, Probabilistic Powerdomains and Quasi-Continuous Domains, Unnamed Item, Unnamed Item, Unnamed Item, Lower topological algebraic domain models of topological spaces, The geometry of conservative programs, Essential and density topologies ons₂-continuous posets, Unnamed Item, A representation of proper BC domains based on conjunctive sequent calculi, Forward analysis for WSTS, part I: completions, A topology on lattice-ordered groups, A unified approach to some non-Hausdorff topological properties, Qualitative versus quantitative fixed point techniques in computer science, Ekeland, Takahashi and Caristi principles in quasi-pseudometric spaces, Nets and reverse mathematics, Uniqueness of directed complete posets based on Scott closed set lattices, Limits in categories of Vietoris coalgebras, On fixed point theory in partially ordered sets and an application to asymptotic complexity of algorithms, Unnamed Item, Unnamed Item, On finiteness properties of Noetherian (Artinian) C*-algebras, Local pre-Hausdorff extended pseudo-quasi-semi metric spaces, Topological semigroups and their prequantale models, A representation of continuous lattices based on closure spaces, Unnamed Item, Quasihomeomorphisms and Skula spaces, Directed Homotopy in Non-Positively Curved Spaces, Local Yoneda completions of quasi-metric spaces, The syntactic side of autonomous categories enriched over generalised metric spaces, (q1,q2)-quasimetric spaces. Covering mappings and coincidence points. A review of the results, A few characterizations of topological spaces with no infinite discrete subspace, Products of topological spaces and families of filters, Unnamed Item, Unnamed Item, Unnamed Item, The monad on strong quasi-metric spaces, Transporting continuity properties from a poset to its subposets, The fixed-point property for represented spaces, Reconstructing étale groupoids from semigroups, \textit{SI}-convergence in \(T_0\) spaces, Some open problems on well-filtered spaces and sober spaces, Sober is not always co-sober, Reverse mathematics, well-quasi-orders, and Noetherian spaces, QRB, QFS, and the probabilistic powerdomain, Grätzer-Hofmann-Lawson-Jung-Sünderhauf duality, Domain-complete and LCS-complete spaces, Algebras of the extended probabilistic powerdomain monad, Some results on poset models consisting of compact saturated subsets, Quasi-continuous Yoneda complete quasi-metric space, \(C_\sigma\)-unique dcpos and non-maximality of the class of dominated dcpos regarding \(\Gamma\)-faithfulness, The duality theory of general \(\mathcal{Z}\)-continuous posets, Distance domains: continuity, Core-compactness, consonance and the Smyth powerspaces, General non-commutative locally compact locally Hausdorff Stone duality, A new dcpo whose Scott topology is well-filtered but not sober, Non-reflective categories of some kinds of weakly sober spaces, On quasi-metrizable \(d\)-spaces, Topological properties of the binary supremum function, Theory of \((q_1,q_2)\)-quasimetric spaces and coincidence points, Completing simple valuations in K-categories, On points of convergence lattices and sobriety for convergence spaces, On Matthews' relationship between quasi-metrics and partial metrics: an aggregation perspective, Alexandroff topologies and monoid actions, Irreducible convergence in \(T_0\) spaces, Sober metric approach spaces, A principal ideal theorem for compact sets of rank one valuation rings, Complements of convex topologies on products of finite totally ordered spaces, Continuity of function spaces from pointwise directed families of characteristic functions., First countability, \( \omega \)-well-filtered spaces and reflections, Fixed points and completeness in metric and generalized metric spaces, Some topological properties of spaces of Lipschitz continuous maps on quasi-metric spaces, Sober Scott spaces are not always co-sober, On \(T_0\) spaces determined by well-filtered spaces, Coincidence of the Isbell and Scott topologies on the function spaces of quasicontinuous domains, Coincidence of the upper Vietoris topology and the Scott topology, On H-sober spaces and H-sobrifications of \(T_0\) spaces, \textbf{K}-reflections of product spaces, Weak algebraic information systems and a new equivalent category of DOM of domains, Representations of stably continuous semi-lattices by information systems and abstract bases, Full abstraction for non-deterministic and probabilistic extensions of PCF. I: The angelic cases, On topologies defined by irreducible sets, Variational principles, completeness and the existence of traps in behavioral sciences, The answer to a problem posed by Zhao and Ho, A Wadge hierarchy for second countable spaces, Thompson aggregators, Scott continuous koopmans operators, and least fixed point theory, Residuated implications derived from quasi-overlap functions on lattices, Sheaves and duality, The relationships between KM-fuzzy quasi-metric spaces and the associated posets of formal balls, Yoneda completion via a dcpo completion of its poset of formal balls, Countably sober spaces, Coincidence points of multivalued mappings in \((q_1,q_2)\)-quasimetric spaces, On topological spaces that have a bounded complete dcpo model, A logic for Lawson compact algebraic L-domains, The probabilistic powerdomain from a topological viewpoint, Maximal classes of spaces and domains determined by topologies on function spaces of domains, On the spectralization of affine and perfectly normal spaces, A discussion of well-filteredness and sobriety, Characterization of posets for liminf convergence being topological, Exponentiable streams and prestreams, Continuous triangular norm based fuzzy topology, The order-sobrification monad, Languages and models for hybrid automata: a coalgebraic perspective, Some characterizations of weak sobriety and upper spaces, Scott approach distance on metric spaces, A comparative study of ideals in fuzzy orders, Existence of well-filterifications of \(T_0\) topological spaces, Continuous L-domains in logical form, Lower topological poset models of \(T_1\) topological spaces, A direct approach to \(K\)-reflections of \(T_0\) spaces, On some kinds of weakly sober spaces, On topological Rudin's lemma, well-filtered spaces and sober spaces, Risk excess measures induced by hemi-metrics, On function spaces related to \(d\)-spaces, First-countability, \( \omega \)-Rudin spaces and well-filtered determined spaces, Kantorovich-Rubinstein quasi-metrics. II: Hyperspaces and powerdomains, On almost sober spaces, Binary metrics, Hausdorff tight groupoids generalised, Chain conditions for graph C*-algebras, Canonical extensions of locally compact frames, Generalized continuous closure spaces. I: Meet preserving closure operations, Lattice-equivalence of convex spaces, Dcpo models of Choquet complete and Baire spaces, Formal ball monads, A representation of FS-domains by formal concept analysis, \(L\)-valued quasi-overlap functions, \(L\)-valued overlap index, and Alexandroff's topology, Two topologies on the lattice of Scott closed subsets, \(SI\)-continuous spaces and continuous posets, On the equivalence of Rudin's lemma and the Boolean prime ideal theorem, Entropy conservation for comparison-based algorithms, Kantorovich-Rubinstein quasi-metrics. III: Spaces of sublinear and superlinear previsions, Characterization of \(T_0\) spaces for liminf convergence being topological, Maximal point spaces of closed interval posets, Bounded complete domains and their logical form, Some notes on spaces of ideals and computable topology