The \(m\)-topology on \(C_{m}(x)\) revisited (Q2493893)

The paper contains some results concerning connections of properties of topological spaces with corresponding properties of spaces of real functions. In Section 2 the authors give some new characterizations of pseudocompactness in terms of \(C_m(X)\). In the third section they classify when \(C_m(X)\) is a weak \(P\)-space, that is, every countable subset is closed. In the fourth section they determine when \(C_m(X)\) has a non-trivial convergent sequence.