Descriptive properties of mappings between nonseparable Luzin spaces

Petr Holický; Václav Komínek

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On projection of nonseparable Souslin and Borel sets along separable spaces

Petr Holický, Václav Komínek (2001)

Acta Universitatis Carolinae. Mathematica et Physica

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Zdeněk Frolík and the descriptive theory of sets and spaces

Petr Holický (1991)

Acta Universitatis Carolinae. Mathematica et Physica

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On analyticity in cosmic spaces

Oleg Okunev (1993)

Commentationes Mathematicae Universitatis Carolinae

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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 $σ$ -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 $C_{p} (X ∣ Y)$ is analytic iff it is a $K_{σ δ}$ -space iff $X$ is $σ$ -compact. ...