# Tag Info

Accepted

### What else (besides the usual) can be said about a Scott Information System if the constructed domain is required to be Hausdorff?

Since the least element $\bot$ of any Scott domain is a compactification point $-$ the only open set containing it is the whole space $-$ the Scott topology is never Hausdorff, unless it is trivial. ...

### An analogue of Scott continuity for infinite-time-Turing-computable functions

The domain-theoretic considerations of the kind you are asking about can be carried out using synthetic domain theory. Related to it is syntehtic topology, and in fact the two share many common ideas. ...
Accepted

### Does the Category of CPOs have omega^op limits?

Here's an attempt (please check!). We have that $\bot_D = d$, where $$d_i = \bigsqcup^{D_i} \{\bot_i,f_i(\bot_{i+1}),f_i(f_{i+1}(\bot_{i+2})),\ldots\}$$ By construction (and monotonicity), the ...
Accepted

### Is there an isomorphism between universal domains $\mathcal{P}\omega$ and the interval domain $\mathbf{I}\mathbb{R}$?

This is only half an answer, but allow me to clear up a constructive point about the interval domain. The usual definition of the interval domain is \mathrm{I}\mathbb{R} = \{[a,b] \mid a, b \in \...
Accepted

### Given a domain, how do we build a language whose denotation is the domain?

As it turns out, the OP is interested in the specific case of the interval domain. Martín Escardó's PhD thesis "PCF extended with real numbers: a domain-theoretic approach to higher-order exact ...
Accepted

### Commutativity of Clock Quantification and Disjunction/Existential Quantification in Guarded Type Theories

Let me first say that I did not look carefully at the second part of your question, nor your sketch of why the clock quantifier should commute with propositional existential quantification. I will ...