In addition to being a complete and utter net.kook
, Alexander Abian would also provide useful information
on that same newsfroup
! His examples on how replacing some axiom
s 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
ing 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.