On the parallel between normality and extremal disconnectedness

DOI10.1016/j.jpaa.2013.10.002zbMath1296.06006OpenAlexW2090162105MaRDI QIDQ392505

Jorge Picado, Javier Gutiérrez García

Publication date: 14 January 2014

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10316/43789

zbMATH Keywords

normalityframeextremal disconnectednesssublocales

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Frames, locales (06D22) Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) (54D15) Real-valued functions in general topology (54C30) De Morgan algebras, ?ukasiewicz algebras (lattice-theoretic aspects) (06D30) Extremally disconnected spaces, (F)-spaces, etc. (54G05)

Related Items (23)

Normal semicontinuity and the Dedekind completion of pointfree function rings ⋮ Perfect locales and localic real functions ⋮ Frame presentations of compact hedgehogs and their properties ⋮ On permutable pairs of quasi-uniformities ⋮ On infinite variants of De Morgan law in locale theory ⋮ A point-free approach to canonical extensions of Boolean algebras and bounded Archimedean \(\ell \)-algebras ⋮ On locales whose countably compact sublocales have compact closure ⋮ A note on weakly pseudocompact locales ⋮ Monotone normality and stratifiability from a pointfree point of view ⋮ Hedgehog frames and a cardinal extension of normality ⋮ On densely normal locales ⋮ Maximal Lindelöf locales ⋮ More on locales in which every open sublocale is \(z\)-embedded ⋮ Some relative normality properties in locales ⋮ On hereditary properties of extremally disconnected frames and normal frames ⋮ Concerning \(P\)-sublocales and disconnectivity ⋮ A unified view of the Dedekind completion of pointfree function rings ⋮ Perfectness in locales ⋮ On classes of localic maps defined by their behavior on zero sublocales ⋮ Gelfand-Naimark-Stone duality for normal spaces and insertion theorems ⋮ Uniform continuity of pointfree real functions via farness and related Galois connections ⋮ A New Approach to the Katětov–Tong Theorem ⋮ More on subfitness and fitness

Cites Work

• Insertion and extension results for pointfree complete regularity
• Extended real functions in pointfree topology
• General insertion and extension theorems for localic real functions
• Permutable pairs of quasi-uniformities
• Rings of real functions in pointfree topology
• Insertion of lattice-valued and hedgehog-valued functions
• On the algebraic representation of semicontinuity
• Pointfree forms of Dowker's and Michael's insertion theorems
• Localic real functions: A general setting
• Completely normal frames and real-valued functions
• Lower and upper regularizations of frame semicontinuous real functions
• Applications of category theory to fuzzy subsets. Based on the eleventh international seminar on fuzzy set theory, held in Linz, Austria, September 1989
• Variants of openness
• A new aspect of the cozero lattice in pointfree topology
• Some characterizations of normal and perfectly normal spaces
• Frames and Locales
• Sandwich-type characterization of completely regular spaces
• First Steps in Descriptive Theory of Locales
• Lebesgue Sets and Insertion of a Continuous Function
• C- and C^*-quotients in pointfree topology
• Perfectness in locales
• Measures on F-Spaces
• Countable Paracompactness and Weak Normality Properties
• A Sufficient Condition for the Insertion of a Continuous Function
• Boundedness Properties in Function-Lattices
• The Normal Completion of the Lattice of Continuous Functions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the parallel between normality and extremal disconnectedness