# Questions tagged [domain-theory]

Domain theory is a branch of order theory that studies partially ordered sets which are called domains. Do not use this tag for questions about the domain of a function.

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### Domain $C^{2+\alpha}$ proprieties

Let $0<\alpha<1$. Hi! I am reading the paper: How to appoximate the heat equation with Neumann Boundary Condition by nonLocal Diffusion Problem (https://link.springer.com/content/pdf/10.1007/...
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### The subspace topology of $Y_u$($Y$ with upper topology) is strictly coarser than the one induced from $X$?

Let $(X,\leqslant )$ be a poset, we define the upper topology has the principle upper sets, that is upper sets of the form $\left \{ \uparrow x:x\in P\right \}$, as the subbase. We can define ...
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### Monotonicity, Continuity and Least fix point of function

I am learning semantics of language Haskell and there i come around this question. For answering this, I am thinking in this way: a) For a function to be monotonic, let's say I have 2 arguments: $f$ ...
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### What is the domain of $f(x,y) = xy/\sqrt{x^2+y^2}$
I think the domain is all real except $(0,0)$, because this point anulates the denominator, but what about with the fact that the limit exists when $(x,y)$ tends to $(0,0)$?
I want to figure out why the Scott topology really forms a topology. In particular, I want to find out why the union of two closed sets is again closed. So say we have a partial order $P = (P, ≤)$. A ...