How to help learners plan a navigation path on the Web is an important issue in web-based learning/education. Our approach to this issue is to allow the learners to preview a sequence of web pages as navigation path plan. In this paper, we introduce an assistant system that enables learners to plan the navigation path in a self-directed way before navigating hyperspace provided by web-based lea...

Let X be a compact metric space and continuous map f:X→X which defines discrete dynamical system (X,f). The f induces two natural maps, namely f¯:K(X)→K(X) on the hyperspace K(X) of non-empty subspaces Zadeh’s extension f^:F(X)→F(X) F(X) normal fuzzy set. In this work, we analyze interaction some orbit tracing properties, specification shadowing properties (X,f) its induced systems (K(X),f¯) (F...

We compute the polynomial entropy of induced maps on hyperspace for a homeomorphism $f$ an interval or circle with finitely many non-wandering points.

We show that if $$(X,d)$$ is a metric space which admits consistent convex geodesic bicombing, then we can construct conical bicombing on $$CB(X)$$ , the hyperspace of nonempty, closed, bounded, and subsets $$X$$ (with Hausdorff metric). If normed or an $$\mathbb {R}$$ -tree, this same method produces . follow by examining nonempty compact assuming proper space.