Aggregate properties of mappings that are associated with the closedness of a graph (in Ukrainian)

V. V. Nesterenko
Yuriy Fedkovych Chernivtsi National University
We study aggregate properties of mappings of two variables that are closed graph relative one of variables. In particular we prove that if $X$ is a topological space, a space $Y$ is a first (second) countable space, $Z$ is a locally compact Hausdorff second countable space, a mapping $f\colon X \times Y \to Z$ such that $f^x$ is continuous for every $x$ with some residual subsets of $X$ and $f_y$ has closed graph for each $y\in Y$, then $C_y(f)=\{x\in X\colon (x, y)\in C(f)\}$ is residual in $X$ for each $y \in Y$ ($C_Y(f)=\{x\in X\colon \{x\}\times Y\subseteq C(f)\}$ is residual in $X$).
continuity; quasi-continuity; cliquishness; horizontally quasi-continuity; transitional function; closed graph
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