Question on sigma-algebras

From: José Carlos Santos (jcsantos_at_fc.up.pt)
Date: 02/27/05 

Date: Sun, 27 Feb 2005 15:01:34 +0000

Hi all:

I would like to know an example of a set X and a sigma-algebra A of
subsets of X such:

1) for any two distinct elements x and y of X, there's some element of A
which contains one of them but not the other one;

2) there's some x in X such that {x} does not belong to A.

Any ideas?

Best regards,

Jose Carlos Santos