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- W4297730281 abstract "We study the existence of continuity points for mappings $f: Xtimes Yto Z$ whose $x$-sections $Yni yto f(x,y)in Z$ are fragmentable and $y$-sections $Xni xto f(x,y)in Z$ are quasicontinuous, where $X$ is a Baire space and $Z$ is a metric space. For the factor $Y$, we consider two infinite point-picking games $G_1(y)$ and $G_2(y)$ defined respectively for each $yin Y$ as follows: In the $n$th inning, Player I gives a dense set $D_nsubset Y$, respectively, a dense open set $D_nsubset Y$, then Player II picks a point $y_ninD_n$; II wins if $y$ is in the closure of ${y_n:ninmathbb N}$, otherwise I wins. It is shown that (i) $f$ is cliquish if II has a winning strategy in $G_1(y)$ for every $yin Y$, and (ii) $f$ is quasicontinuous if the $x$-sections of $f$ are continuous and the set of $yin Y$ such that II has a winning strategy in $G_2(y)$ is dense in $Y$. Item (i) extends substantially a result of Debs (1986) and item (ii) indicates that the problem of Talagrand (1985) on separately continuous maps has a positive answer for a wide class of small compact spaces." @default.
- W4297730281 created "2022-09-30" @default.
- W4297730281 creator A5022254475 @default.
- W4297730281 date "2010-10-03" @default.
- W4297730281 modified "2023-09-26" @default.
- W4297730281 title "Cliquishness and Quasicontinuity of Two Variables Maps" @default.
- W4297730281 doi "https://doi.org/10.48550/arxiv.1010.0441" @default.
- W4297730281 hasPublicationYear "2010" @default.
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