On lattice-valued frames: The completely distributive case
References (10)
- et al.
Insertion of lattice-valued and hedgehog-valued functions
Topol. Appl.
(2006) - et al.
Uniform-type structures on lattice-valued spaces and frames
Fuzzy Sets and Systems
(2008) Fuzzy topological spaces and fuzzy compactness
J. Math. Anal. Appl.
(1976)- et al.
Category theoretic aspects of chain-valued frames: part I: categorical and presheaf theoretic foundations
Fuzzy Sets and Systems
(2008) - et al.
Category theoretic aspects of chain-valued frames: part II: applications to lattice-valued topology
Fuzzy Sets and Systems
(2008)
Cited by (15)
A general categorical reflection for various completions of Q-closure spaces and Q-ordered sets
2023, Fuzzy Sets and SystemsSober topological spaces valued in a quantale
2022, Fuzzy Sets and SystemsCitation Excerpt :Different extensions of the notion of sobriety to the fuzzy context have been proposed since 1990. To mention a few: Rodabaugh [26], Zhang and Liu [42], Kotzé [14], Srivastava and Khastgir [30], Pultr and Rodabaugh [24,25], Gutiérrez García, Höhle and de Prada Vicente [5], Yao [37,38], Jäger and Yao [9], Singh and Srivastava [29], and etc. In these works, the table of truth-values is assumed to be a complete Heyting algebra (i.e., a frame), sometimes even a completely distributive lattice.
A categorical isomorphism between injective balanced L-S<inf>0</inf>-convex spaces and fuzzy frames
2022, Fuzzy Sets and SystemsOn fuzzy monotone convergence Q-cotopological spaces
2021, Fuzzy Sets and SystemsCitation Excerpt :Existing literature on the subject usually choose to work with open sets to extend sobriety to fuzzy topological spaces. It has been studied by many researchers with fruitful results, including Rodabaugh [18], Zhang and Liu [30], Kotzé [9,10], Srivastava and Khastgir [20], Pultr and Rodabaugh [13–16], Gutiérrez García, Höhle and de Prada Vicente [5], and Yao [24,25], etc. Recently, D. Zhang [29] established a theory of sobriety for quantale-valued cotopological spaces based on irreducible closed sets.
Overlap and grouping functions on complete lattices
2021, Information SciencesCitation Excerpt :In this section, we recall some fundamental concepts related to the theory of lattices which shall be needed in the sequel. ([26]) Let L be completely distributive lattice. Then L is a frame.
Frames of continuous functions
2020, Topology and its Applications