El espacio de Golomb y su no conexidad en pequeño

• Autores: José del Carmen Alberto Domínguez, Gerardo Acosta, Gerardo Delgadillo Piñón, Maira Madriz Mendoza
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 35, Nº. 2, 2017, págs. 189-213
• Idioma: español
• DOI: 10.18273/revint.v35n2-2017004
• Títulos paralelos:
  • The Golomb space and its non connectedness "im kleinen"
• Enlaces
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• Resumen
  • español

    En el presente trabajo, estudiamos los espacios de Brown, que son conexos y no completamente de Hausdorff. Utilizando progresiones aritméticas, construimos una base BG para una topología τG de N, y mostramos que (N, τG), llamado el espacio de Golomb, es de Brown. También probamos que hay elementos de BG que son de Brown, mientras que otros están totalmente separados. Escribimos algunas consecuencias de este resultado. Por ejemplo, (N, τG) no es conexo en pequeño en ninguno de sus puntos. Esto generaliza un resultado probado por Kirch en 1969. También damos una prueba más simple de un resultado presentado por Szczuka en 2010.

  • English

    In the present paper we study Brown spaces which are connected and not completely Hausdorff. Using arithmetic progressions, we construct a base BG for a topology τG on N, and show that (N, τG), called the Golomb space is a Brown space. We also show that some elements of BG are Brown spaces, while others are totally separated. We write some consequences of such result. For example, the space (N, τG) is not connected "im kleinen" at each of its points. This generalizes a result proved by Kirch in 1969. We also present a simpler proof of a result given by Szczuka in 2010.

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