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Weak P‐points and Cancellation in β S
Author(s) -
FILALI MAHMOUD
Publication year - 1996
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1996.tb49164.x
Subject(s) - countable set , mathematics , cancellative semigroup , semigroup , compactification (mathematics) , combinatorics , closure (psychology) , discrete mathematics , pure mathematics , law , political science
ABSTRACT: Let S be a cancellative semigroup and let β S be the Stone‐Čech compactification of S . Then β S is a semigroup with an operation which extends that of S and which is continuous only in one variable. The points s of S are easily shown to be right (left) cancellative in β S , i.e., ys and zs ( sy and sz ) are different elements of β S whenever y and z are. It is known that such a property is not valid for all the elements of β S\S . However, we will see that the set of points in β S\S which are cancellative in β S is dense in β S\S . In particular, we will see that the (weak) p‐points of β S\S , which are contained in the closure of some countable subset of S , are (right) cancellative in β S .