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!

  1. 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.