<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332013000100006</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Sobre una construcción de un monoide libre con identidad sobre un topos E con el objeto de los números naturales]]></article-title>
<article-title xml:lang="en"><![CDATA[About the construction of a free monoid with identity on a topos E with the object of natural numbers]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Acuña Ortega]]></surname>
<given-names><![CDATA[Osvaldo]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad de Costa Rica Escuela de Matemática CIMPA]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>01</month>
<year>2013</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>01</month>
<year>2013</year>
</pub-date>
<volume>20</volume>
<numero>1</numero>
<fpage>79</fpage>
<lpage>94</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332013000100006&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332013000100006&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332013000100006&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Damos una construcción del monoide libre con identidad sobre un objeto X, M (X ). Donde]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[We proved that the free monoid with identify in X is]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Teoría de topos]]></kwd>
<kwd lng="es"><![CDATA[objetos K-finitos]]></kwd>
<kwd lng="es"><![CDATA[números naturales]]></kwd>
<kwd lng="en"><![CDATA[Topoi]]></kwd>
<kwd lng="en"><![CDATA[K-finite objects]]></kwd>
<kwd lng="en"><![CDATA[natural numbers]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <div style="text-align: justify; font-family: verdana;">     <div style="text-align: center;"><font style="font-weight: bold;"  size="4">Sobre una construcci&oacute;n&nbsp; de un&nbsp; monoide libre con identidad&nbsp; sobre un topos <span style="font-style: italic;">E</span> con el objeto de los&nbsp; n&uacute;meros naturales</font><br style="font-weight: bold;"> <font style="font-weight: bold;" size="2"></font><br  style="font-weight: bold;"> <font style="font-weight: bold;" size="4">About&nbsp; the&nbsp; construction&nbsp; of a free monoid with identity on a topos<span style="font-style: italic;"> E&nbsp; </span>with the&nbsp; object&nbsp; of natural&nbsp; numbers</font>    <br> </div>     <br>     <div style="text-align: center;"><font size="2">Osvaldo Acu&ntilde;a Ortega<sup><a href="#Afiliacion1">*</a><a name="Afiliacion2"></a>+</sup></font>    <br> </div> <font size="2"><a href="#correspondencia">    <br> </a><a name="Correspondencia2"></a>*<a href="#Correspondencia1">Direcci&oacute;n para correspondencia</a></font>    <br> <hr style="width: 100%; height: 2px;"><font style="font-weight: bold;"  size="3">Resumen</font>    <br> <font size="2"></font>    <br> <font size="2">Damos&nbsp; una&nbsp; construcci&oacute;n&nbsp; del monoide&nbsp; libre con identidad&nbsp; sobre un objeto <span style="font-style: italic;">X, M (X )</span>.&nbsp; Donde</font>    ]]></body>
<body><![CDATA[<br> <font size="2"></font>    <br>     <div style="text-align: center;"><img alt=""  src="/img/revistas/rmta/v20n1/a06f1.jpg"  style="width: 530px; height: 45px;">    <br> </div> <font size="2"></font>    <br> <font size="2"><span style="font-weight: bold;">Palabras&nbsp; clave:</span> Teor&iacute;a de topos, objetos K&#8211;finitos, n&uacute;meros naturales.</font>    <br> <font size="2"></font>    <br> <font style="font-weight: bold;" size="3">Abstract</font>    <br> <font size="2"></font>    <br> <font size="2">We proved&nbsp; that the free monoid with identify in X&nbsp; is</font>    <br> <font size="2"></font>    ]]></body>
<body><![CDATA[<br>     <div style="text-align: center;"><img alt=""  src="/img/revistas/rmta/v20n1/a06f2.jpg"  style="width: 542px; height: 45px;">    <br> </div> <font size="2"></font>    <br> <font size="2"><span style="font-weight: bold;">Keywords:</span> Topoi, K&#8211;finite objects, natural numbers.    <br>     <br> <span style="font-weight: bold;">Mathematics Subject Classification:</span> 03G30, 18B25.    <br> </font> <hr style="width: 100%; height: 2px;"><font size="2">    <br> Ver contenido disponible en pdf    <br> </font><font size="2"></font>    <br> <hr style="width: 100%; height: 2px;"><font style="font-weight: bold;"  size="3">Referencias</font>    ]]></body>
<body><![CDATA[<br> <font size="2"></font>    <!-- ref --><br> <font size="2">[1]&nbsp; Acu&ntilde;a&#8211;Ortega,&nbsp; O.&nbsp; (1977)&nbsp; <span style="font-style: italic;">Finiteness in&nbsp; Topoi</span>,&nbsp; Ph.&nbsp; D. Dissertation, Wesleyan University, Middletown, CT.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1948800&pid=S1409-2433201300010000600001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font>    <br> <font size="2"></font>    <!-- ref --><br> <font size="2">[2]&nbsp; Acu&ntilde;a&#8211;Ortega, O. (2011) &#8220;Una&nbsp; nota sobre objetos k &#8722; f initos en un topos&nbsp; Booleano&nbsp; con el objeto de los n&uacute;meros naturales&#8221;, R<span style="font-style: italic;">evista&nbsp; de Matem&aacute;tica:&nbsp; Teor&iacute;a y Aplicaciones</span>&nbsp; 19(2):&nbsp; 239&#8211;245.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1948803&pid=S1409-2433201300010000600002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font>    <br> <font size="2"></font>    <!-- ref --><br> <font size="2">[3]&nbsp; Acu&ntilde;a&#8211;Ortega, O.; Linton, F.E.J. (1979) &#8220;Finiteness and decidability I&#8221;,&nbsp; in:&nbsp;&nbsp; <span  style="font-style: italic;">Applications&nbsp; of Sheaves</span>,&nbsp; Lecture&nbsp; Notes&nbsp; in Mathematics&nbsp; 753, Springer&#8211;Verlag, New York:&nbsp; 80&#8211;100.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=1948806&pid=S1409-2433201300010000600003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font>    <br> <font size="2"></font><font size="-1">    ]]></body>
<body><![CDATA[<br> <a name="Correspondencia1"></a><a href="#Correspondencia2">*</a>Correspondencia a:    <br> </font><font size="2">Osvaldo Acu&ntilde;a Ortega. </font><font  size="2">CIMPA&nbsp; &amp; Escuela&nbsp; de Matem&aacute;tica, Universidad de Costa Rica, 2060 San Jos&eacute;, Costa Rica.    <br> </font><font size="2"><a name="Afiliacion1"></a><a href="#Afiliacion2">*</a> CIMPA&nbsp; &amp; Escuela&nbsp; de Matem&aacute;tica, Universidad de Costa Rica, 2060 San Jos&eacute;, Costa Rica.</font>    <br>     <div style="text-align: center;"><font size="2"><span  style="font-weight: bold;"></span></font> <hr style="width: 100%; height: 2px;"><font size="2"><span  style="font-weight: bold;">Received: 17/May/2012; Revised: 4/Dec/2012; Accepted:&nbsp; 5/Dec/2012</span> </font></div> </div>      ]]></body><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Acuña-Ortega]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
</person-group>
<source><![CDATA[Finiteness in Topoi]]></source>
<year>1977</year>
</nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Acuña-Ortega]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
</person-group>
<article-title xml:lang="es"><![CDATA[&#8220;Una nota sobre objetos k &#8722; f initos en un topos Booleano con el objeto de los números naturales&#8221;]]></article-title>
<source><![CDATA[Revista de Matemática: Teoría y Aplicaciones]]></source>
<year>2011</year>
<volume>19</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>239-245</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Acuña-Ortega]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
<name>
<surname><![CDATA[Linton]]></surname>
<given-names><![CDATA[F.E.J.]]></given-names>
</name>
</person-group>
<source><![CDATA[&#8220;Finiteness and decidability I&#8221;]]></source>
<year>1979</year>
<page-range>80-100</page-range><publisher-loc><![CDATA[^eNew York New York]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
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