Strengthening connected Tychonoff topologies

• Shakhmatov, Dimitri ^[1] ; Tkachenko, Mikhail ^[2] ; Tkachuk, Vladimir V. ^[2] ; Wilson, Richard G. ^[2]
  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.