In the context of possibly infinite computations yielding finite or infinite (binary) outputs, the space 2≤ω = 2∗∪2ω appears to be one of the most fundamental spaces in Computer Science. Though underconsidered, next to 2, this space can be viewed (§3.5.2) as the simplest compact space native to computer science. In this paper we study some of its properties involving topology and computability....

The paper considers algebraic directed-complete partial orders with a semi-regular Scott topology, called regular domains. As is well known, the category of Scott domains and continuous maps is Cartesian closed. This is no longer true, if the domains are required to be regular. Two Cartesian closed subcategories of the regular Scott domains are exhibited: regular dI-domains with stable maps and...

We examine the problem of extending, in a natural way, order-preserving maps that are de ̄ned on the interior of a closed cone K1 (taking values in another closed cone K2 ) to the whole of K1 . We give conditions, in considerable generality (for cones in both ̄niteand in ̄nite-dimensional spaces), under which a natural extension exists and is continuous. We also give weaker conditions under which ...

Let X denote a locally compact metric space and φ : X → X be a continuous map. In the 1970s L. Zadeh presented an extension principle, helping us to fuzzify the dynamical system (X, φ), i.e., to obtain a map Φ for the space of fuzzy sets on X. We extend an idea mentioned in [P. Diamond, A. Pokrovskii, Chaos, entropy and a generalized extension principle, Fuzzy Sets and Systems 61 (1994)] and we...

Aim of this present paper is, we introduce and investigate neutrosophic Z-continuous maps which is a new kind continuous in topological spaces. Also discussed about some properties characterization Z-irresolute maps.