In addition to being a complete and utter

net.kook on

`sci.math`, Alexander Abian would also provide

useful information on that same

newsfroup! His examples on how replacing some

axioms of very simple theories of sets (limited versions of

set theory) were somewhat simplistic, but often

interesting. He also helped many a

poster with understanding various

fixed point properties; his still-extant

homepage gives a "

universal" fixed point

theorem (he calls it "most

fundamental") that doesn't require a

topology or

ordering on the set.

^{1}
Truly an interesting person!

- He uses ordinals to analyse the structure of iteration of a map on a set; you might consider the order (and induced topology) "cheating", in that they impose structure on the set. However, this structure is natural.