A space is said to be of dimension zero, one, two or three as it comprises of a single point, line, plane or contains points not all of which are co-planers.
‘Space’ shall mean a three -dimensional space.
Some Axioms on Space
Space is a non-empty set of points.
(ii) Axiom -2:
If are distinct points in space then and if is a plane containing then
(iii) Axiom -3:
Given any three non-collinear point in space is exactly one plane such that
(iv) Axiom -4:
If are two distinct planes in a space and is a point such that then there exists another point different from such that
A subset of a space is said to be a Convex set if, for all . Otherwise it is not a convex set.
(v) Axiom -5:
If is a plane is space then the point of not contianed in are divided into two disjoint non-empty convex sets such that
If a point belongs to space we also say that the point lies on/in that space.