Navigation (colloquially known as “surfing”) is the activity of following links and browsing web pages. This is a time intensive activity engaging all web users seeking information. We often get “lost in hyperspace” when we lose the context in which we are browsing, giving rise to the infamous navigation problem. So, in this age of information overload we need navigational assistance to help us...

In the context of exploring educational hypermedia on the World Wide Web, this paper presents a history visualization that helps learners reorganize explored contents to find what Web sites they should visit next. Learning-by-exploration is discussed as it relates to educational hypermedia, including the "Get Lost in Hyperspace" problem, learning support approaches, and current work on hypermed...

The point-to-set principle of J. Lutz and N. (2018) has recently enabled the theory computing to be used answer open questions about fractal geometry in Euclidean spaces $\mathbb{R}^n$. These are classical questions, meaning that their statements do not involve computation or related aspects logic. In this paper we extend reach from arbitrary separable metric $X$. We first two dimensions--com...

Let M be the collection of all intersections of balls, considered as a subset of the hyperspace H of all closed, convex and bounded sets of a Banach space, furnished with the Hausdorff metric. We prove that M is uniformly very porous if and only if the space fails the Mazur intersection property.

Given a map of a solenoid homotopic to the identity, we use its difference from the identity to study its rotation and the nature of its fixed point set. With the aid of hyperspace theory, we show that a certain class of solenoids admits no expansive homeormorphism.

The main issue addressed in this paper is how to improve the coordination between navigational learning process and its meta-cognitive process in hyperspace provided by existing Web resources, which includes coordinating two different meta-cognitive processes: navigation planning and reflection. This paper demonstrates the cognitive tool, which enables learners to reify and coordinate their nav...