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.
@article{118568,
author = {Oleg Okunev},
title = {On analyticity in cosmic spaces},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {34},
year = {1993},
pages = {185-190},
zbl = {0837.54009},
mrnumber = {1240216},
language = {en},
url = {http://dml.mathdoc.fr/item/118568}
}
Okunev, Oleg. On analyticity in cosmic spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 185-190. http://gdmltest.u-ga.fr/item/118568/
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