Stone Spaces

Johnstone, P. T. (1982). Stone Spaces. Cambridge University Press.

Type

Book

Intellectual base

Review or monograph

Year

1982

ISBN

9780521238939

Link

https://openlibrary.org/books/OL3484997Mmatched

Cited by

6 citations across 6 artifacts.

Each citation links to the sentence it supports in the citing article.

Domain-specific

• Complete Heyting algebra
  • A complete Heyting algebra, or frame, is a complete lattice in which finite meets distribute over arbitrary joins; equivalently each meet map has a right adjoint defining Heyting implication.
• Locally Hausdorff space
  • … identity and a convenient observable transfers from The line with two origins is locally Euclidean and locally Hausdorff but its two origins cannot be separated by disjoint global neighborhoods. to An étale space may be locally Hausdorff over a Hausdorff base while global gluing leaves distinct germs inseparable..
• Normal space
  • … observable transfers from Every metric space is normal because positive distance functions can construct disjoint neighborhoods of disjoint closed sets. to A proof states whether normal includes T1, verifies closedness and disjointness, then constructs neighborhoods rather than inferring normality from Hausdorffness..
• Open Set
  • the substrate for program meanings. Computability theory and logic — open sets correspond to semi-decidable sets and, under Stone duality and intuitionistic semantics, to provable propositions

    This sourceStone duality between topological and lattice-theoretic structure, which underwrites the open-set/provable-proposition correspondence.

• Saturated set (intersection of open sets)
  • … A canonical instance directly demonstrates that the set equals its topological saturation under the declared specialization-order orientation and is an arbitrary intersection of open subsets. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, dataset, or implementation..
• Stone duality
  • The entry centers the classical Boolean duality and maps named extensions; it does not merge all categorical dualities into a single theorem or suppress constructive qualifications.

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