Geodesic
A note on condensations of $C_p(X)$ onto compacta
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 3, pp. 485-492 Cet article a éte moissonné depuis la source 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.
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.
Classification : 54A25, 54A35, 54C35, 54D30
Keywords: condensation; compactum; network; Lindelöf space; topology of pointwise convergence; $\sigma $-compact space; Eberlein compactum; Corson compactum; Borel set; monolithic space; tightness 
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     author = {Arhangel'skii, A. V. and Pavlov, O. I.},
     title = {A note on condensations of $C_p(X)$ onto compacta},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {485--492},
     year = {2002},
     volume = {43},
     number = {3},
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     zbl = {1090.54003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2002_43_3_a7/}
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Arhangel'skii, A. V.; Pavlov, O. I. A note on condensations of $C_p(X)$ onto compacta. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 3, pp. 485-492. http://geodesic.mathdoc.fr/item/CMUC_2002_43_3_a7/