Geodesic
Searching for more absolute CR-epic spaces
Theory and applications of categories, Tome 22 (2009), pp. 54-76.

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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.
Classification : 18A20, 54C45, 54B30
Keywords: absolute CR-epics, countable neighbourhood property, Alster's condition Dieudonne plank 
@article{TAC_2009_22_a2,
     author = {Michael Barr and John F. Kennison and R. Raphael},
     title = {Searching for more absolute {CR-epic} spaces},
     journal = {Theory and applications of categories},
     pages = {54--76},
     publisher = {mathdoc},
     volume = {22},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2009_22_a2/}
}
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Michael Barr; John F. Kennison; R. Raphael. Searching for more absolute CR-epic spaces. Theory and applications of categories, Tome 22 (2009), pp. 54-76. http://geodesic.mathdoc.fr/item/TAC_2009_22_a2/