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A Note on Minimal Separating Function Sets

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Abstract

We study point-separating function sets that are minimal with respect to the property of being separating. We first show that for a compact space X having a minimal separating function set in Cp(X) is equivalent to having a minimal separating collection of functionally open sets in X. We also identify a nice visual property of X2 that may be responsible for the existence of a minimal separating function family for X in Cp(X). We then discuss various questions and directions around the topic.

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Authors and Affiliations

  1. Miami, Florida, USA

    Raushan Buzyakova

  2. Facultad de Ciencias Físico-Matematicas, Benemérita Universidad Autonoma de Puebla, Apdo postal 1152, Puebla, Puebla, CP 72000, Mexico

    Oleg Okunev

Authors
  1. Raushan Buzyakova
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  2. Oleg Okunev
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Corresponding authors

Correspondence to Raushan Buzyakova or Oleg Okunev.

Additional information

(Submitted by S. N. Tronin)

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Buzyakova, R., Okunev, O. A Note on Minimal Separating Function Sets. Lobachevskii J Math 40, 149–155 (2019). https://doi.org/10.1134/S1995080219020057

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  • DOI: https://doi.org/10.1134/S1995080219020057

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