Notes on Point-Free Topology

DOI10.1007/978-3-030-84319-9_6zbMath1486.18018OpenAlexW3206443722MaRDI QIDQ5861652

Jorge Picado, Ales Pultr

Publication date: 1 March 2022

Published in: New Perspectives in Algebra, Topology and Categories (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-84319-9_6

zbMATH Keywords

category of framesHeyting algebrasober spacepoint-free topologycategory of locales

Mathematics Subject Classification ID

Frames, locales (06D22) Research exposition (monographs, survey articles) pertaining to general topology (54-02) Research exposition (monographs, survey articles) pertaining to category theory (18-02) Frames and locales, pointfree topology, Stone duality (18F70)

Cites Work

• Measure, randomness and sublocales
• Remainders in pointfree topology
• Gattungen von lokalen Strukturen
• Stone-Čech compactification of locales. II
• Presenting the frame of the unit circle.
• Spatial sublocales and essential primes
• Lattice-equivalence of topological spaces
• Modal operators on Heyting algebras
• Paracompactness revisited
• Separation axioms and frame representation of some topological facts
• Adjoint maps between implicative semilattices and continuity of localic maps
• A presentation of the assembly of a frame by generators and relations exhibits its bitopological structure.
• On weak lattice and frame homomorphisms
• Frames and Locales
• An extension of the Galois theory of Grothendieck
• Lindelöf locales and realcompactness
• The Duality of Distributive Continuous Lattices
• Spaces with Boolean assemblies
• The point of pointless topology
• Tychonoff's theorem without the axiom of choice
• The Spectral Theory of Distributive Continuous Lattices
• ON THE COMPLETION OF NEARNESS FRAMES
• CAUCHY POINTS OF UNIFORM AND NEARNESS FRAMES
• Separation in Point-Free Topology
• Hewitt’s irresolvability and induced Sublocales in spatial frames
• Axiom $T_D$ and the Simmons sublocale theorem
• Notes on the Product of Locales
• Atomless Parts of Spaces.
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