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
(i) Axiom-1:
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
CONVEX SET
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
Note:
If a point belongs to space we also say that the point lies on/in that space.