A note on condensations of $C_p(X)$ onto compacta
Arhangel'skii, Aleksander V. ; Pavlov, Oleg I.
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002), p. 485-492 / Harvested from Czech Digital Mathematics Library
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A condensation is a one-to-one continuous mapping onto. It is shown that the space $C_p(X)$ 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 $C_p(X)$ condenses onto a metrizable compactum (Theorem 10). Several curious open problems are formulated.

Publié le : 2002-01-01
Classification:  54A25,  54A35,  54C35,  54D30 
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     author = {Aleksander V. Arhangel'skii and Oleg I. Pavlov},
     title = {A note on condensations of $C\_p(X)$ onto compacta},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {43},
     year = {2002},
     pages = {485-492},
     zbl = {1090.54003},
     mrnumber = {1920523},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119337}
}

Arhangel'skii, Aleksander V.; Pavlov, Oleg I. A note on condensations of $C_p(X)$ onto compacta. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 485-492. http://gdmltest.u-ga.fr/item/119337/

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