Real Algebraic and Analytic Geometry

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110. Michael Barr, John F. Kennison, Robert Raphael:
Searching For Absolute CR-Epic Spaces.

e-mail: , ,

Submission: 2005, September 16.

In two previous papers, [Barr, Burgess, & Raphael (2003), Barr, Raphael, & Woods (to appear)], some of us have investigated the situation of a topological space Y and a subspace X such that the induced map C(X) --> C(Y ) is an epimorphism in the category CR of commutative rings. We call such an embedding a CR-epic embedding. We continue this investigation. The most notable result finds a condition on a space Lindel÷f X that guarantees that X is CR-epic in every embedding. This condition is stable under finite products, countable sums, and the formation of closed subspaces and cozero subspaces. We also get further results in the non-Lindel÷f case that are suffcient to show the DieudonnÚ plank and some closely related spaces are absolute CR-epic.

Mathematics Subject Classification (2000): 18A20, 54C45, 54B30.

Keywords and Phrases: absolute CR-epic, compact P-supports, DieudonnÚ plank.

Full text, 25p.: pdf 253k.

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