Dubrovnik VI – Geometric Topology September 30 – October 7, 2007
	ABSTRACTS	pdf-version of this abstract

Kazuhiro Kawamura
University of Tsukuba, Japan

Compacta with algebraically closed function algebras

For a compact Hausdorff space X, C(X) denotes the algebra consisting of all complex-valued continuous functions on X. We say that C(X) is algebraically closed if each monic algebraic equation with C(X)-coefficients has a root in C(X). We discuss the characterization problem of compacta X with algebraic closed C(X).

REFERENCES

[1] N. Brodskiy, J. Dydak, A. Karasev and K. Kawamura. Root closed function algebras on compacta of large dimensions, Proc. Amer. Math. Soc. 35 (2007), 587–596.
[2] K. Kawamura and T. Miura. On the root closedness of continuous function algebras, preprint.
[3] K. Kawamura, a paper in preparation.