Certain observations on a \(\mathrm{U}_\mathrm{fin}\)-type selection principle (Q6551370)

The study of selection principles is well-known and recently several papers have been devoted to this topic. Weaker versions of the selection principles have also been investigated extensively by several researchers. In this article a generalization of the selection principle \(\mathrm{U}_{\mathrm{fin}} (\mathcal{O}, \Omega)\), denoted by \(\mathrm{U}_{\mathrm{fin}}(\mathcal{O}, \overline{\Omega})\), is introduced and studied. In particular, the authors study the connection of \(\mathrm{U}_{\mathrm{fin}}(\mathcal{O}, \overline{\Omega})\) with the other similar properties, give some characterization results by considering mappings into the Baire space and present several results concerning critical cardinalities.