Network-based space layouts are fine-grained models of architectural spaces. They include rich spatial relationships between layout elements. Such information tends to be limited in existing space representations in building information modeling (BIM) systems. Network-based space layouts could be useful in the space planning and building automation domains. Their main feature is a geometric net...

In this paper the idea of -locally closed sets in generalized topological space is introduced and study some of their properties. We introduce the notion of (,’)locally closed continuous functions on generalized topological space and investigate some of their characterizations.

We characterize weak continuity of an interval order on a topological space (X, τ) by using the concept of a scale in a topological space. Mathematics Subject Classification: 06A06; 54F05; 91B16

Algorithmic randomness over general spaces has been considered such as an effective topological space and a computable metric space. In this paper we generalize algorithmic randomness to a computable topological space. First we define computable measures on a computable topological space and study computability of the evaluation. Next we define randomnesses via three approaches. Measure randomn...