Category theoretic aspects of chain-valued frames. II: Applications to lattice-valued topology

DOI10.1016/j.fss.2007.07.012zbMath1170.18005OpenAlexW2051043980MaRDI QIDQ834494

Ales Pultr, Stephen E. Rodabaugh

Publication date: 26 August 2009

Published in: Fuzzy Sets and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.fss.2007.07.012

zbMATH Keywords

completenesscocompleteness\(L\)-frames\(L\)-Frm\(L\)-Loc\(L\)-top\(L\)-topological spacesanti-stratified/stratified spacescharacteristic/Martin/stratification functorsfactorization structuresimage/preimage operatorsiota/omega functorsspectrum functorsuniversal/co-universal spacesupper/lower forgetful functorsupper/lower free functors

Mathematics Subject Classification ID

Related Items (21)

Fundamental duality of abstract categories and its applications ⋮ Category theoretic aspects of chain-valued frames. I: Categorical and presheaf theoretic foundations ⋮ Uniform-type structures on lattice-valued spaces and frames ⋮ Sobriety and spatiality in varieties of algebras ⋮ Bounded sobriety and k-bounded sobriety of Q-cotopological spaces ⋮ A categorical isomorphism between injective balanced \(L\)-\(S_0\)-convex spaces and fuzzy frames ⋮ On fuzzy monotone convergence \(\mathcal{Q}\)-cotopological spaces ⋮ Overview and comparison of localic and fixed-basis topological products ⋮ Hypergraph functor and attachment ⋮ Category-theoretic fuzzy topological spaces and their dualities ⋮ On the uniformization of lattice-valued frames ⋮ Composite variety-based topological theories ⋮ Sobriety and spatiality in categories of lattice-valued algebras ⋮ On lattice-valued frames: the completely distributive case ⋮ Necessity of non-stratified and anti-stratified spaces in lattice-valued topology ⋮ From quantale algebroids to topological spaces: fixed- and variable-basis approaches ⋮ Generalized fuzzy topology versus non-commutative topology ⋮ Variable-basis topological systems versus variable-basis topological spaces ⋮ Sobriety of quantale-valued cotopological spaces ⋮ Completely primeL-filters, irreducibleL-filters and sobriety ⋮ On ordered categories as a framework for fuzzification of algebraic and topological structures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Point-set lattice-theoretic topology
• Category theoretic aspects of chain-valued frames. I: Categorical and presheaf theoretic foundations
• Fuzzy sets and sheaves. I: Basic concepts
• Relationship of algebraic theories to powerset theories and fuzzy topological theories for lattice-valued mathematics
• Lowen, para-Lowen, and \(\alpha\)-level functors and fuzzy topologies on the crisp real line
• Fuzzy topology. II: Product and quotient spaces
• Applications of category theory to fuzzy subsets. Based on the eleventh international seminar on fuzzy set theory, held in Linz, Austria, September 1989
• Fuzzy topological spaces and fuzzy compactness
• Topological and algebraic structures in fuzzy sets. A handbook of recent developments in the mathematics of fuzzy sets
• Triangular norms
• Functorial relationships between lattice-valued topology and topological systems

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