I have a doubt about the construction of the suspension of the sphere of dimension -1, that is the empty set. In the following image I try to explain the suspension of the empty set:
My doubt is that I think that the "part" of the empty set that result of the product of one of the endpoints of the line with the empty space is collapsed with a point and we proceed in this way with the other remaining point, but the empty space no have points, then, where the points come from? Am I correct with the thinking of collapse the empty space with a point "two times"?