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@IgorKhavkine In Italian there is also "pennello di luce" (paintbrush of light), presumably introduced in 19th century optics and still used today in that field (compare also with "pennello di elettroni" for electron beam).
@FernandoMuro Apologies, I didn't read the May-Sigurdsson reference. I found Puppe's ref through tom Dieck's monograph. Did anybody look into that Bourbaki's reference anyway?
Puppe (p.336 in Math. Zeitschrift Vol. 69) claims without proof that they are not homeomorphic and refers to a similar example in Bourbaki Top. Gen. Ch.1 §9 Exer.11 (1951 edition). I could not track down this reference though.
I have always suspected pencil to be a mistranslation from the corresponding French mathematical term pinceau (brush, which makes more sense when you think of a pencil of curves as a bunch of bristles held together). However, my Oxford dictionary says pencil means fine paintbrush in Middle English.
@Florian point well taken; I cautiously wrote 'precluding most of the local-global machinery' but your example suggests this sort of principle might be implemented in pretopological spaces as well. Next week I'll try to get my hands on "General topology" by Császár as it might contain some information about this issue.
