At 23:07 -0700 2/09/2002, Tim May wrote: >You say you prefer continuity and connectedness....this all depends >on the topology one chooses. In the microcircuit case, the natural >topology of circuit elements and conductors and clock ticks gives us >our lattice points. In other examples, set containment gives us a >natural poset, without "points." > >(In fact, of course mathematics can be done with open sets, or >closed sets for that matter, as the "atoms" of the universe, with no >reference to points, and certainly not to Hausdorff spaces similar >to the real number continuum.) > >The really interesting things, for me, are the points of >intersection between logic and geometry.
I agree with all your points. Do you know the book by VICKERS: TOPOLOGY VIA LOGIC. It is an introductory book on locale and quantale. It is written in the spirit of category theory although he helps the non categorial readers by mentioning them only in notes. Bruno