the topology and the topology

[chrisamaphone]

sometimes i learn things about topology with pictures or by taping together pieces of paper. i think about stretching, shrinking, and numbers of holes.

sometimes i try to learn about topology by understanding a series of mathematical definitions. i think about partial orders, closed and open sets, frames, interiors, and neighborhoods.

at what point do these lessons converge?

Comments

[wjl.livejournal.com]

I have no idea, but i like this post :D

[jcreed.livejournal.com]

Well, I'd like to be able to say that if you could tell me how tightly you want them to be related to each other, I could tell you how long it would take to explain it sufficiently well... ;)

[roseandsigil.livejournal.com]

jcreed you are the best

[neelk]

Today, Prakash Panangaden told me that one approach to this question is via the Lawson topology on domains. This is a finer topology than the Scott topology, and has the property that it is Hausdorff and metrizable, unlike the Scott topology (in general).

Unfortunately, many of the relevant papers (such as, er, Lawson's) seem to be not on the web or behind paywalls. :(