A mob is a word used for a topological semigroup which is a Hausdorff space. A clan is a compact connected mob with a two-sided identity element.
Who used these words with these meanings first and when? Why were these words chosen? I'm guessing it's a play on "group", but is it really?
Best Answer
The mob/clan terminology goes back to Alexander Wallace:
A note on mobs (1952).
The structure of topological semigroups (1953).