Our main result in this paper is that a Banach space X embeds into L, if and only if l~(X) embeds into Lo; more generally if 1 _-< p < 2, X embeds into Lp if and only if lp (X) embeds into L~,.

The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. Our recent mathematical formalization of this framework is capable of representing correlations between different domains in a geometric way. In this paper, we extend our f...

we study algebraic properties of categories of merotopic, nearness, and filter algebras. we show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. the forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...

We will give a combinatorial description of the homotopy groups for the suspension ofK(π, 1) and wedges of 2-spheres. In particular, all of the homotopy groups of the 2-sphere are given as the centers of certain combinatorially described groups.

The level of satisfaction and effectiveness of 3D virtual learning environments were examined. Additionally, 3D virtual learning environments were compared with face-to-face learning environments. Students that experienced higher levels of flow and presence also experienced more satisfaction but not necessarily more effectiveness with 3D virtual learning environments. There were no significant ...