Strengthening connected Tychonoff topologies


  • Dimitri Shakhmatov Ehime University
  • Mikhail Tkachenko Universidad Autónoma Metropolitana
  • Vladimir V. Tkachuk Universidad Autónoma Metropolitana
  • Richard G. Wilson Universidad Autónoma Metropolitana



Connected, Strongly σ-discrete, Submetrizable, Regular open set, Dense subset, Topological group, Quotient group, Free topological group


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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Author Biographies

Dimitri Shakhmatov, Ehime University

Department of Mathematics, Faculty of Sciences

Mikhail Tkachenko, Universidad Autónoma Metropolitana

Departamento de Matemáticas

Vladimir V. Tkachuk, Universidad Autónoma Metropolitana

Departamento de Matemáticas

Richard G. Wilson, Universidad Autónoma Metropolitana

Departamento de Matemáticas


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How to Cite

D. Shakhmatov, M. Tkachenko, V. V. Tkachuk, and R. G. Wilson, “Strengthening connected Tychonoff topologies”, Appl. Gen. Topol., vol. 3, no. 2, pp. 113–131, Oct. 2002.



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