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Certain Observations on a \({{\,\mathrm{U_{fin}}\,}}\)-Type Selection Principle

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Abstract

A weaker variant of the selection principle \({{\,\mathrm{U_{fin}}\,}}({\mathcal {O}},\Omega ),\) namely \({{\,\mathrm{U_{fin}}\,}}({\mathcal {O}},\overline{\Omega }),\) is investigated in this article. We present situations where \({{\,\mathrm{U_{fin}}\,}}({\mathcal {O}},\Omega )\) behaves differently from \({{\,\mathrm{U_{fin}}\,}}({\mathcal {O}},\overline{\Omega }).\) Few characterization results are obtained by considering mappings into the Baire space. Several results are presented concerning critical cardinalities. In particular, we perform investigations assuming near coherence of filters (NCF) and semifilter trichotomy. Besides, \({{\,\mathrm{U_{fin}}\,}}({\mathcal {O}},\overline{\Omega })\) is characterized using weakly groupable and related covers. We also exhibit certain game theoretic observations.

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Acknowledgements

The authors are thankful to the referee(s) for numerous useful comments and suggestions that considerably improved the presentation of the paper.

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  1. Department of Mathematics, University of Gour Banga, Malda, West Bengal, 732103, India

    Debraj Chandra & Nur Alam

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  1. Debraj Chandra
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  2. Nur Alam
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Correspondence to Debraj Chandra.

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Communicated by Mohammad Reza Koushesh.

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Chandra, D., Alam, N. Certain Observations on a \({{\,\mathrm{U_{fin}}\,}}\)-Type Selection Principle. Bull. Iran. Math. Soc. 50, 9 (2024). https://doi.org/10.1007/s41980-023-00851-y

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