The <i>κ</i> -Fréchet-Urysohn property for <i> C _p </i> ( <i>X</i> ) is equivalent to baireness of <i>B</i> ₁ ( <i>X</i> )

Abstract A topological space X is Baire if the intersection of any sequence of open dense subsets of X is dense in X . In this paper, we establish that the property ( κ ) for a Tychonoff space X is equivalent to Baireness of B 1 ( X ), and hence, the Banakh property for C p ( X ) is equivalent to meagerness of B 1 ( X ). Thus, we obtain one characteristic of the Banakh property for C p ( X ) through the property of the space X .