Space is the logical embodiment of the requirement that each point be unique. If two or more points occupy the same place they are 'congruent', i.e. the same point because they are indistinguishable and congruent as opposed to differentiable and congruent. To differentiate more than one point requires the insertion of some non-point material.
The simplest manifold which encompasses all the foregoing is a 'ray' beginning at (0,1) and proceeding to infinity through a one dimensional space counting points in consecutive order (time).