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On the coincidence of set-open and uniform topologies

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Abstract

The ℝ-compactness property is studied, and criteria are established for the coincidence of the set-open topology and the topology of uniform convergence on the spaces of continuous functions.

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References

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Division of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620219, Russia

    S. E. Nokhrin & A. V. Osipov

Authors
  1. S. E. Nokhrin
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  2. A. V. Osipov
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Corresponding author

Correspondence to S. E. Nokhrin.

Additional information

Original Russian Text © S.E. Nokhrin, A.V. Osipov, 2009, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Vol. 15, No. 2.

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Nokhrin, S.E., Osipov, A.V. On the coincidence of set-open and uniform topologies. Proc. Steklov Inst. Math. 267 (Suppl 1), 184–191 (2009). https://doi.org/10.1134/S0081543809070165

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  • DOI: https://doi.org/10.1134/S0081543809070165

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