Date: Mar 14, 2013 10:49 PM
Author: William Elliot
Subject: Stone Cech

Let (g,Y) be a Cech Stone compactification of S.
If (f,X) is a compactification of S, does X embed in Y?

If (g,Y) is a compactification of S and
for all compactifications (f,X), X embeds in Y
is (g,Y) a Stone Cech compactification of S?

Why in the heck is a compactification an embedding
function and a compact space? Wouldn't be simpler
to define a compactification of a space S, as a
compact space into which S densely embeds?