14 Sept 2004
2:30 - 4:00   M Barr
Characterizing Lindelof absolute CR-epics.

Abstract: There have been several talks during the past year or so by John
Kennison and me on absolute CR-epic spaces, which are spaces X such that
for any embedding X --> Y, the induced map C(Y) --> C(X) on the
real-valued function rings is epic in the category CR of commutative
rings.  In his last talk, Kennison introduced a concept we called CNP (for
countable neighbourhood property) that says that the intersection of any
countable family of beta X-neighbourhoods of X is also a beta
X-neighbourhood of X.  Kennison showed that Lindelof CNP space is absolute
CR-epic, but otherwise did not emphasize the property.  Now, following an
ingeneous suggestion of R. Levy we have shown that for Lindelof spaces,
CNP is equivalent to absolute CR-epic.  I will attempt to make this talk
self-contained by proving both halves of the equivalence.

It is worth mentioning that, while there are absolute CR-epic spaces that
are not Lindelof, a necessary (but not sufficient) condition on such a
space X is that be embeddable in a Lindelof absolute CR-epic space Y in
such a way that C(X) = C(Y) and |Y-X| = 1.