Hoops in R(exp 3)

摘要

Hoops are defined as geometric circles of radius = 1 in 3-dimensional Euclidean space R(exp 3). It is shown that it is possible to continuously fill an open set of R(exp 3) with disjoint hoops. It is also shown that in any such open set, every pair of hoops must link each other, and consequently there is an upper bound to the volume that such an open set may have.