Abstract
Many categories of semantic domains can be considered from an order-theoretic point of view and from a topological point of view via the Scott topology. The topological point of view is particularly fruitful for considerations of computability in classical spaces such as the Euclidean real line. When one embeds topological spaces into domains, one requires that the Scott continuous maps between the host domains fully capture the continuous maps between the guest topological spaces. This property of the host domains is known as injectivity. For example, the continuous Scott domains are characterized as the injective spaces over dense subspace embeddings (Dana Scott, 1972, 1980). From a third point of view, the continuous Scott domains arise as the algebras of a monad (Wyler, 1985). The topological characterization by injectivity turns out to follow from the algebraic characterization and general category theory (Escardó 1998). In this paper we systematically consider monads that arise in semantics and topology, obtaining new proofs and discovering new characterizations of semantic domains and topological spaces by injectivity.
Original language | English |
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Pages (from-to) | 229-244 |
Number of pages | 16 |
Journal | Electronic Notes in Theoretical Computer Science |
Volume | 20 |
DOIs | |
Publication status | Published - 1999 |
Event | MFPS XV, Mathematical Foundations of Programming Semantics, Fifteenth Conference - New Orleans, LA, United States Duration: 28 Apr 1999 → 1 May 1999 |
Keywords
- Continuous lattice
- Continuous Scott domain
- Domain theory
- Flat embedding
- Injective space
- Kock-Zöberlein monad
- L-domain
- Stably locally compact space
ASJC Scopus subject areas
- Theoretical Computer Science
- General Computer Science