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A.V. Arhangel’skii, O.I. Pavlov ) JA  ?@AI=JEI B C

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A.V. Arhangel’skii, O.I. Pavlov

A note on condensations of

Cp(X)

onto compacta

Comment.Math.Univ.Carolinae 43,3 (2002) 485-492.

Abstract: A condensation is a one-to-one continuous mapping onto. It is shown that the spaceCp(X) of real-valued continuous functions on X in the topology of pointwise convergence very often cannot be condensed onto a compact Hausdorff space. In particular, this is so for any non-metrizable Eberlein compactum X (Theorem 19). However, there exists a non-metrizable compactum X such that Cp(X) condenses onto a metrizable compactum (Theorem 10). Several curious open problems are formulated.

Keywords: condensation, compactum, network, Lindel¨of space, topology of point- wise convergence,σ-compact space, Eberlein compactum, Corson compactum, Borel set, monolithic space, tightness

AMS Subject Classification: Primary 54A25, 54C35, 54A35

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