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En este artículo presentamos una caracterización de las curvas de Peano como límite uniforme de sucesiones de curvas α-densas en el compacto que es llenado por la curva de Peano. Estas curvas α-densas deben tener densidades tendiendo a cero y sus funciones coordenadas deben de ser de variación tendiendo a infinito cuando α tiende a cero.
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