i'm trying to get my head around what a mathematical space is, like euclidean or minkowski. i was trying to understand some of the less intuitive ones and realised i'm not so sure what a space actually is. when i read such hard to understand stuff being called a space, it doesn't feel obvious anymore.
is it just a structure that can be addressed by coordinates? are its properties actually properties of the vectors it contains and the coordinates come from comparing them, or are the contained vectors pinned against some reference grid? does a scalar space make sense? i can't work out what i'm misunderstanding.