On the \(T_{1}\) axiom and other separation properties in constructive point-free and point-set topology

DOI10.1016/j.apal.2009.03.005zbMath1223.03050OpenAlexW1992760717WikidataQ114016295 ScholiaQ114016295MaRDI QIDQ636295

Giovanni Curi, Peter Aczel

Publication date: 26 August 2011

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

Full work available at URL: https://doi.org/10.1016/j.apal.2009.03.005

zbMATH Keywords

constructive type theoryformal spaceconstructive set theorypoint-free topologyconstructive topologypoint-set topologyseparation properties

Mathematics Subject Classification ID

Constructive and recursive analysis (03F60) Topological spaces and generalizations (closure spaces, etc.) (54A05) Frames, locales (06D22)

Related Items (7)

Unnamed Item ⋮ Exact approximations to Stone-Čech compactification ⋮ On Tarski’s fixed point theorem ⋮ Locatedness and overt sublocales ⋮ Topological inductive definitions ⋮ On some peculiar aspects of the constructive theory of point-free spaces ⋮ On the existence of Stone-Čech compactification

Cites Work

• Exact approximations to Stone-Čech compactification
• Constructive metrisability in point-free topology.
• Aspects of general topology in constructive set theory
• On the collection of points of a formal space
• Maximal and partial points in formal spaces
• A ‘ T1’ space with no closed points, and a “ T1” locale which is not ‘ T1 ’
• Lattice Aspects of Radical Ideals and Choice Principles
• T1-locales
• The lattice theoretic part of topological separation properties
• Atomless Parts of Spaces.
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