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.

选择原则的较弱变体\({{\,\mathrm{U_{fin}}\,}}({\mathcal {O}},\Omega ),\)即\({{\,\mathrm{本文研究了U_{fin}}\,}}({\mathcal {O}},\overline{\Omega }),\) 。我们提出\({{\,\mathrm{U_{fin}}\,}}({\mathcal {O}},\Omega )\)与\({{\,\mathrm{U_{ fin}}\,}}({\mathcal {O}},\overline{\Omega }).\)通过考虑映射到贝尔空间，几乎无法获得表征结果。提出了一些关于临界基数的结果。特别是，我们假设滤波器（NCF）和半滤波器三分法接近相干，进行研究。此外，\({{\,\mathrm{U_{fin}}\,}}({\mathcal {O}},\overline{\Omega })\)使用弱可分组和相关覆盖来表征。我们还展示了某些博弈论观察结果。