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$Σ$ -products and selections of set-valued mappings

Ivailo Shishkov — 2001

Commentationes Mathematicae Universitatis Carolinae

Every lower semi-continuous closed-and-convex valued mapping $Φ : X \to 2^{Y}$ , where $X$ is a $Σ$ -product of metrizable spaces and $Y$ is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.

Hereditarily normal Katětov spaces and extending of usco mappings

Ivailo Shishkov — 2000

Commentationes Mathematicae Universitatis Carolinae

Several classes of hereditarily normal spaces are characterized in terms of extending upper semi-continuous compact-valued mappings. The case of controlled extensions is considered as well. Applications are obtained for real-valued semi-continuous functions.

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Σ -products and selections of set-valued mappings

Hereditarily normal Katětov spaces and extending of usco mappings

$Σ$ -products and selections of set-valued mappings