Ok, sorry once again for the long wait times for these posts - ive promised myself to post more regularly from the 1st of august

So lets try describe an abstact space where we can do geometry. For starters, as i mentioned earlier, we need it to look like normal euclidean space (at least locally) so that we can talk about calculus and thus lengths of curves and other fun things. So lets recall some topology

A topological space is calledhausdorffif for any two points x and y (with x not equal to y) of the space we can find two disjoint open neighbourhoods of those points.

So we want our abstact spaces to be hausdorff (so the topology can distinguish points in it), for two important reasons. The first is easy to see, we want to model our abstract idea on normal euclidean geometry but the other more important reason will have to wait for a bit.

Now do you know what it means for a set to be countable wallaby?