These are the slides for a presentation at the New York City Category Seminar on October 19, 2009, about a peculiar topological space that Peter
Johnstone, Bob Paré and I used some 30 years ago to solve a
"Short"? — Could actually be presented in well under a half-hour.
"Peculiar"? — this space has a discrete, dense, open subset, whose (closed) complement is a discrete subspace as well, yet ...
"Topoidal problem"? — ... the whole space admits a double cover with no continuous global section.
Seemed like the sort of mix of areas NYC Category Theory Seminar participants would appreciate. And the pictures may be a pleasant diversion, too :-) .
To see it, go here. (For other stuff, go here.)