A characterization of 𝜎-compactness of a cosmic space 𝑋 by means of subspaces of 𝑅^{𝑋}

Arhangel’skii, A.; Calbrix, J.

doi:10.1090/S0002-9939-99-04782-6

A characterization of $\sigma$-compactness of a cosmic space $X$ by means of subspaces of $R^X$
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by A. V. Arhangel’skii and J. Calbrix PDF

Proc. Amer. Math. Soc. 127 (1999), 2497-2504 Request permission

Abstract:

This work is devoted to the relationship between topological properties of a space $X$ and those of $C_{p}(X)$ (= the space of continuous real-valued functions on $X$, with the topology of pointwise convergence). The emphasis is on $\sigma$-compactness of $X$ and on location of $C_{p}(X)$ in $R^{X}$. In particular, $\sigma$-compact cosmic spaces are characterized in this way.

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