User:Leigh.Samphier/OrderTheory
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Order Theory (Completed)
- Definitions related to Order Theory can be found here.
- Results about Order Theory can be found here.
- Definitions related to Semilattices can be found here.
- Results about Semilattices can be found here.
- Definitions related to Join Semilattices can be found here.
- Results about Join Semilattices can be found here.
- Definitions related to Meet Semilattice can be found here.
- Results about Meet Semilattices can be found here.
- Definitions related to Lattice Theory can be found here.
- Results about Lattice Theory can be found here.
<...> is the dual statement of <...> by Dual Pairs (Order Theory).
So <...> follows from the Duality Principle.
Sources
- 1967: Saunders Mac Lane and Garrett Birkhoff: Algebra: Chapter XIV Lattices : $\S 1$ Posets: Duality Principle
- 1971: George A. Grätzer: Lattice Theory: Chapter $1$: First Concepts, $\S 6$: Special Elements
- 1982: Peter T. Johnstone: Stone Spaces: Chapter $\text I$: Preliminaries, Definition $1.2$ and $1.4$
- 2012: Jorge Picado and Aleš Pultr: Frames and Locales: Chapter $1$: Spaces and Lattices of Open Sets, $\S 1$ Sober spaces, Definition $1.1$
To Be Published
Frames & Locales
User:Leigh.Samphier/OrderTheory/Definition:Category of Compact Regular Locales
User:Leigh.Samphier/OrderTheory/Definition:Completely Regular Locale
User:Leigh.Samphier/OrderTheory/Definition:Compact Completely Regular Locale
User:Leigh.Samphier/OrderTheory/Definition:Category of Compact Completely Regular Locales