#
Searching for more absolute CR-epic spaces

##
Michael Barr, John F. Kennison, and R. Raphael

We continue our examination of absolute CR-epic spaces, or spaces with the
property that any embedding induces an epimorphism, in the category of
commutative rings, between their rings of continuous functions. We
examine more closely the deleted plank construction, which generalizes the
Dieudonne construction, and yields absolute CR-epic spaces which are not
Lindelof. For the Lindelof case, an earlier paper has shown the
usefulness of the countable neighbourhood property, CNP, and the Alster
condition (where CNP means that the space is a P-space in any
compactification and the Alster condition says that any cover of the space
by $G_\delta$ sets has a countable subcover, provided each compact subset
can be covered by a finite subset.) In this paper, we find further
properties of Lindelof CNP spaces and of Alster spaces, including
constructions that preserve these properties and conditions equivalent to
these properties. We explore the outgrowths of such spaces and find
several examples that answer open questions in our previous work.

Keywords:
absolute CR-epics, countable neighbourhood property, Alster's condition
Dieudonne plank

2000 MSC:
18A20, 54C45, 54B30

*Theory and Applications of Categories,*
Vol. 22, 2009,
No. 3, pp 54-76.

http://www.tac.mta.ca/tac/volumes/22/3/22-03.dvi

http://www.tac.mta.ca/tac/volumes/22/3/22-03.ps

http://www.tac.mta.ca/tac/volumes/22/3/22-03.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/3/22-03.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/3/22-03.ps

Revised 2009-07-15. Original version at

http://www.tac.mta.ca/tac/volumes/22/3/22-03a.dvi

TAC Home