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Strengthening connected Tychonoff topologies

    1. [1] Ehime University

      Ehime University

      Japón

    2. [2] Universidad Autónoma Metropolitana

      Universidad Autónoma Metropolitana

      México

  • Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 3, Nº. 2, 2002, págs. 113-131
  • Idioma: inglés
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  • Resumen
    • The problem of whether a given connected Tychonoff space admits a strictly finer connected Tychonoff topology is considered. We show that every Tychonoff space X satisfying ω (X) ≤ c and c (X) ≤ N0 admits a finer strongly σ-discrete connected Tychonoff topology of weight 2c. We also prove that every connected Tychonoff space is an open continuous image of a connected strongly σ-discrete submetrizable Tychonoff space. The latter result is applied to represent every connected topological group as a quotient of a connected strongly σ-discrete submetrizable topological group.


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