Ukrainian Mathematical Journal, Volume (69), No (2), Year (2017-9) , Pages (1224-1231)

#### Title : ( points of upper and lower semi-continuity of multi-valued functions )

Authors: Seyyed Alireza Kamel Mirmostafaee ,

Citation: BibTeX | EndNote

#### Abstract

In this paper, we will investigate joint upper and lower semi-continuity of two-variable set-valued functions. More precisely. among other results, we will show that under certain conditions, a two-variable lower horizontally quasi-continuous mapping $F:X \times Y \to \mathcal{K}(Z)$ is jointly upper semi-continuous on sets of the from $D \times \{y_0\}$, where $D$ is a dense $G_\delta$ subset of $X$ and $y_0 \in Y$. Similar result for joint lower semi-continuity of upper horizontally quasi-continuous mappings is obtained. These will improve some known results on joint continuity of single-valued functions.

#### Keywords

, set-valued functions, quasi-continuous, categorically continuous, developable spaces.
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@article{paperid:1062369,
author = {Kamel Mirmostafaee, Seyyed Alireza},
title = {points of upper and lower semi-continuity of multi-valued functions},
journal = {Ukrainian Mathematical Journal},
year = {2017},
volume = {69},
number = {2},
month = {September},
issn = {0041-5995},
pages = {1224--1231},
numpages = {7},
keywords = {set-valued functions; quasi-continuous; categorically continuous; developable spaces.},
}

%0 Journal Article
%T points of upper and lower semi-continuity of multi-valued functions
%A Kamel Mirmostafaee, Seyyed Alireza
%J Ukrainian Mathematical Journal
%@ 0041-5995
%D 2017