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Volume 34 • Number 3 • 2011
• On the Semigroup of Semi-Continuous Interval-Valued Multihomomorphisms
S. Chaopraknoi and Y. Kemprasit

A characterization of semi-continuous interval-valued multihomomorphisms on $(\mathbb{R},+)$ has been given as follows: An interval-valued multifunction $f$ on $\mathbb{R}$ is a semi-continuous multihomomorphism on $(\mathbb{R},+)$ if and only if $f$ is one of the following forms: $f(x)=\{cx\}$, $f(x)=\mathbb{R}$, $f(x)=(0,\infty)$, $f(x)=(-\infty,0)$, $f(x)=[cx,\infty)$ and $f(x)=(-\infty,cx]$ where $c$ is a constant in $\mathbb{R}$. Denote by SIM$(\mathbb{R},+)$ the set of all such multifunctions on $\mathbb{R}$. We show that SIM$(\mathbb{R},+)$ is a semigroup under composition and it is a regular semigroup.

2010 Mathematics Subject Classification: 20E25, 20M17.

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