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

Author 
math.analysis.chnu@gmail.com
Yuriy Fedkovych Chernivtsi National University

Abstract 
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 $X$).

Keywords 
continuity; quasicontinuity; cliquishness; horizontally quasicontinuity; transitional function;
closed graph

DOI 
doi:10.15330/ms.43.1.2735

Reference 
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Pages 
2735

Volume 
43

Issue 
1

Year 
2015

Journal 
Matematychni Studii

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