In a 3D two-tone digital space, the conditions under which sequential
transformation of an object point to a non-object point, or its invers
e, does not affect the image topology are investigated. The concept of
border-connectivity is introduced and an efficient algorithm for chec
king a simple point is proposed. In this connection, some other intere
sting properties of 3D digital geometry are also discussed. This inves
tigation may be used in thinning and topology preserving morphological
transformations in 3D digital space.