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Relative version of star-Hurewicz property

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Abstract

We study preservation properties of relatively star-Hurewicz property under two mappings and in Alexandroff space. For a topological space X, the collection of relatively star-Hurewicz subspaces of X is an admissible \(\sigma\)-ideal in X. The characterizations of relatively star-Hurewicz spaces given using selection principles. For a paracompact space X, TWO has a winning strategy in the star-Hurewicz game on X if and only if TWO has a winning strategy in the Hurewicz game on X. In this manner we obtain relationships of relatively star-Hurewicz property with other existing Hurewicz properties in literature.

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Acknowledgement

The authors are thankful to the referee for careful reading and suggestions that helped to improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Delhi, New Delhi, 110007, India

    M. Bhardwaj & S. Singh

  2. Department of Mathematics, Atmaram Sanatan Dharma College, University of Delhi, New Delhi, 110021, India

    B. K. Tyagi

Authors
  1. M. Bhardwaj
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  2. S. Singh
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  3. B. K. Tyagi
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Correspondence to M. Bhardwaj.

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The first author acknowledges the fellowship grant of University Grant Commission, India.

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Bhardwaj, M., Singh, S. & Tyagi, B.K. Relative version of star-Hurewicz property. Acta Math. Hungar. 164, 85–100 (2021). https://doi.org/10.1007/s10474-020-01121-7

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  • DOI: https://doi.org/10.1007/s10474-020-01121-7

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