Real Algebraic and Analytic Geometry |

On CR-epic embeddings and absolute CR-epic spaces.

e-mail: , ,

Submission: 2004, October 6.

*Abstract:
We study Tychonoff spaces $X$ with the property that, for all
topological embeddings $X\to Y $, the induced map $C(Y)
\to C(X)$ is an epimorphism of rings. Such spaces are called
\good. The simplest examples of \good spaces are $\sigma$-compact
locally compact spaces and \Lin $P$-spaces. First countable
spaces must be locally compact in order to be \good.
However, a ``bad'' class of \good spaces is exhibited whose pathology
settles, in the negative, a number of open questions. Spaces which are
not \good abound, and some are presented. Many open questions remain.*

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

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