First and foremost, I am aware that a similar question has been asked here and has been touched upon elsewhere. I have found these discussions very compelling but a bit light on external reference, and so wanted to approach the topic on different terms and in one place.
As such, I was wondering if anyone might have recommendations for material on the history of constructions of 'mathematical spaces.' By this, I do not mean a 'mathematical space' in perhaps the most restrictive formal sense, i.e., a set with additional structure. I have a more general interest in the history which pertains to the placement of objects—real numbers, shapes, etc.—in relation to one another. I realize, to some of you this may sound the same; I simply mean to say that I wish to approach this topic rather permissively. In this vein, if anyone sees it fit to bring up material on the history of coordinate systems, geometry, rings, groups, lattices or whatever else, I would more than welcome it.
I've seen this question approached as a topological one—which I suppose it must be to some extent. However, to be clear, if the question were approached as such, I would not be so much interested in the history of topology as the history of the various spaces which topology has studied.
In particular, I'm very interested to learn of alternative spaces which may have developed in antiquity, so material which deals with the more distant past is very much appreciated.
As an aside: I am, at least in part, inspired by the Euler Spiral, Ulam Spiral and other kinds of 'spiral space' which have received some, shall I say, more recent attention. That said, I am curious to learn of even more 'out there' ways of constructing mathematical space.