Non-Hausdorff Topology and Domain Theory
Electronic supplements to the book
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  • About Me
  • Addenda
    • Consonance
    • Countability
    • Counterexamples
    • Domains and orders
    • Equilogical spaces
    • Filters
    • Locales, sublocales, nuclei
    • Models of topological spaces
    • Noetherian spaces and variants
    • Powerdomains and hyperspaces
    • Projective limits
    • Quasi-Polish spaces
    • Quasicontinuity, Locally Finitary Compact Spaces
    • Quasi-uniform spaces
    • Streams, prestreams, and d-spaces
    • Topological functors
    • Topological semilattices
    • Well-filteredness
    • ————————————
    • Another form of Stone duality
    • Bernstein subsets of R
    • Bitopological spaces and stable compactness
    • Borel sets, analytic sets, and the Baire property
    • Chains and nested spaces
    • Domains XII
    • Forbidden substructures
    • Integration
    • Irredundant families, the Smyth powerdomain, the Lyu-Jia theorem, and the baby Groemer theorem
    • Pointwise directed families of maps
    • Shimrat’s theorem
    • Sober subspaces and the Skula topology
    • TD spaces
    • The Rasiowa-Sikorski lemma and the Baire property
    • Weakly Hausdorff spaces, and locally strongly sober spaces
  • Errata
  • Course Ideas
  • Open Problems
  • Puzzles

Domains and orders

Here is the list of posts on domains and posets, as opposed to more general topological spaces, so far:

  1. Bourbaki, Witt, and Dito Pataraia
  2. Quasi-continuous dcpos and locally finitary compact spaces
  3. Iwamura’s lemma, Markowsky’s theorem and ordinals
  4. Coherence of dcpos
  5. Well-filtered dcpos
  6. Markowsky or Cohn?
  7. FS-domains of discs and formal balls
  8. Dcpos and convergence spaces I: Scott and Heckmann convergences
  9. Dcpos and convergence spaces II: preserving products
  10. Bc-hulls and Clat-hulls
  11. Quotients, colimits of dcpos, and related matters
  12. Dcpos built as graphs of functions
  13. X. Jia’s well-filtered, non-sober dcpo
  14. Quasi-Polish spaces and rounded ideal completions
  15. Zhao, Xi, and Chen’s well-filtered, non-sober dcpo
  16. Plotkin’s powerdomain and the hedgehog
  17. L-domains, stable open sets, and stable Stone duality
  18. A report from ISDT’22: one-step closure; c-spaces are not CCC
  19. Scott’s formula

— Jean Goubault-Larrecqjgl-2011

  • Recent Posts

    • We’ve moved!
    • Compact semilattices without small semilattices II: Gierz’s counterexample
    • Compact semilattices without small semilattices I: interval homomorphisms, products, and the Hoare hyperspace
    • Scott’s formula
    • The fundamental theorem of compact semilattices
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