Geodesic
On analyticity in cosmic spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 1, pp. 185-190
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We prove that a cosmic space (= a Tychonoff space with a countable network) is analytic if it is an image of a $K$-analytic space under a measurable mapping. We also obtain characterizations of analyticity and $\sigma $-compactness in cosmic spaces in terms of metrizable continuous images. As an application, we show that if $X$ is a separable metrizable space and $Y$ is its dense subspace then the space of restricted continuous functions $C_p(X\mid Y)$ is analytic iff it is a $K_{\sigma \delta }$-space iff $X$ is $\sigma $-compact.
We prove that a cosmic space (= a Tychonoff space with a countable network) is analytic if it is an image of a $K$-analytic space under a measurable mapping. We also obtain characterizations of analyticity and $\sigma $-compactness in cosmic spaces in terms of metrizable continuous images. As an application, we show that if $X$ is a separable metrizable space and $Y$ is its dense subspace then the space of restricted continuous functions $C_p(X\mid Y)$ is analytic iff it is a $K_{\sigma \delta }$-space iff $X$ is $\sigma $-compact.
Classification : 54C35, 54C50, 54E20, 54H05
Keywords: measurable mapping; cosmic space; analyticity; topology of pointwise convergence 
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     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {185--190},
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Okunev, Oleg. On analyticity in cosmic spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 1, pp. 185-190. http://geodesic.mathdoc.fr/item/CMUC_1993_34_1_a18/