On condensations of 𝐶_{𝑝}-spaces onto compacta

Arhangel’skii, A.

doi:10.1090/S0002-9939-00-05758-0

On condensations of $C_{p}$-spaces onto compacta
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by A. V. Arhangel’skii PDF

Proc. Amer. Math. Soc. 128 (2000), 1881-1883 Request permission

Erratum: Proc. Amer. Math. Soc. 130 (2002), 1875-1875.

Abstract:

A condensation is a one-to-one onto mapping. It is established that, for each $\sigma$-compact metrizable space $X$, the space $C_{p}(X)$ of real-valued continuous functions on $X$ in the topology of pointwise convergence condenses onto a metrizable compactum. Note that not every Tychonoff space condenses onto a compactum.

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