A spread extension associated with Madden-type generators |
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Authors: | Hlengani J Siweya |
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Institution: | (1) Department of Mathematics, University of Limpopo, Private Bag X1106, Sovenga, South Africa |
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Abstract: | Summary A frame homomorphism <InlineEquation ID=IE"3"><EquationSource Format="TEX"><!CDATA<InlineEquation ID=IE"4"><EquationSource
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L\to M$ between locally connected frames is called a \emph{localic spread} if $\bigcup\limits_{u\in L}S_{u}$ is a basis for
$M$, where <InlineEquation ID=IE"1"><EquationSource Format="TEX"><!CDATA<InlineEquation ID=IE"2"><EquationSource Format="TEX"><!CDATA$$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>
S_{u}=\{x\in M\mid x\Leqq_{c}f(u)\} $$ for each $u\in L$, where $x\Leqq_{c}h(u)$ denotes that ``$x$ is a component of $h(u)$'.
Madden-type generators and relations are applied on $L$ to form a freely generated frame $CM$ induced by $j\: M\to CM$ leading
to a \emph{spread extension} $j\circ f\: L\to CM$ of~$f$. In this article, we discuss properties of a local spread extension
(which is not complete) between locally connected frames. |
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Keywords: | (relative local) connectedness freely generated frame (localic) spread extension |
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