Commun. Korean Math. Soc. 2002 Vol. 17, No. 4, 647-673 Printed December 1, 2002

Jang-Hwan Im Chung-Ang University

Abstract : There are many models to study topological $R^2$-planes. Unlike topological $R^2$-planes, it is difficult to find models to study topological $R^3$-spaces. If an 4-dimensional affine plane intersects with $R^3$, we are able to get a geometrical structure on $R^3$ which is similar to $R^3$-space, and called $R^2$-divisible $R^3$-space. Such spatial geometric models is useful to study topological $R^3$-spaces. Hence, we introduce some classes of topological $R^2$-divisible $R^3$-spaces {\linebreak} which are induced from 4-dimensional affine planes.