Una aproximación a la noción de homotopía entre espacios toplógicos finitos desde las funciones submodulares
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En este trabajo se estudian las conexiones entre las FD relaciones con soporte finito y los preórdenes. Se demuestra que existe una correspondencia biunívoca entre las FD relaciones con soporte finito y los espacios pretopológicos finitos, y se aprovecha dicho vínculo para interpretar, en terminos de las funciones submodulares, aquellos conceptos relacionados con la clasificación por tipo de homotopía de los espacios topológicos finitos: función continua, espacio conexo, espacio T0 y beat points. Ademas, se presentan algoritmos que calculan los valores de algunas funciones sub-modulares relacionadas con espacios topológicos finitos y se interpreta el algoritmo de reducción´ de Stong [13] por medio de dichas funciones. Los resultados obtenidos se basan principalmente en [2], [4], [11] y [14].
Abstract In this work the connections between the FD relations with finite support and preorders are studied. We show that there is a one to one correspondence between the FD relations with finite support and pretopologicos finite spaces , and that link is used to interpret, in terms of functions submodulares ´ those concepts related to homotopy type classification of finite topological spaces continuous function, connected space, space T0 and beat points. Furthermore , algorithms that compute the values of some functions related submodulares finite topological spaces and Stong reduction algorithm [13] through interprets these functions are presented . The results are mainly based on [2], [4], [11] and [14].
Abstract In this work the connections between the FD relations with finite support and preorders are studied. We show that there is a one to one correspondence between the FD relations with finite support and pretopologicos finite spaces , and that link is used to interpret, in terms of functions submodulares ´ those concepts related to homotopy type classification of finite topological spaces continuous function, connected space, space T0 and beat points. Furthermore , algorithms that compute the values of some functions related submodulares finite topological spaces and Stong reduction algorithm [13] through interprets these functions are presented . The results are mainly based on [2], [4], [11] and [14].