Small spaces which ‘‘generate” large spaces

Large Caps in Small Spaces

We construct large caps in projective spaces of small dimension (up to 11) defined over fields of order at most 9. The constructions are both theoretical and computer-supported. Some more computergenerated 4-dimensional caps over larger fields are also mentioned.

Large Cardinals and Small Dowker Spaces

We prove that, if there is a model of set-theory which contains no first countable, locally compact, scattered Dowker spaces, then there is an inner model which contains a measurable cardinal. A Hausdorff space is normal if, for every pair of disjoint closed sets C and D, there is a pair of disjoint open sets, U containing C and V containing D. A (normal) space is binormal if its product with t...

Small Valdivia Compact Spaces

We prove a preservation theorem for the class of Valdivia compact spaces, which involves inverse sequences of “simple” retractions. Consequently, a compact space of weight 6 א1 is Valdivia compact iff it is the limit of an inverse sequence of metric compacta whose bonding maps are retractions. As a corollary, we show that the class of Valdivia compacta of weight 6 א1 is preserved both under ret...

Navigating large virtual spaces

INTRODUCTION As important as navigation is to human performance in virtual worlds, support for effective navigation is often overlooked in the design process. This document reports an experiment intended to show that real-world wayfinding and environmental design principles are effective in designing virtual worlds which support skilled wayfinding behavior. The design principles are adapted fro...

Large Homogeneous Compact Spaces