A note on Volterra and Baire spaces

In Proposition 2.6 in (G‎. ‎Gruenhage‎, ‎A‎. ‎Lutzer‎, ‎Baire and Volterra spaces‎, ‎\textit{Proc‎. ‎Amer‎. ‎Math‎. ‎Soc.} {128} (2000)‎, ‎no‎. ‎10‎, ‎3115--3124) a condition that‎ ‎every point of D D is G δ Gδ in X X was overlooked‎. ‎So we‎ ‎proved some conditions by which a Baire space is equivalent to a‎ ‎Volterra space‎. ‎In this note we show that if X X is a‎ ‎monotonically normal T 1 T1 -space with countable pseudocharacter ‎and X X has a σ σ -discrete dense subspace D D ‎, ‎then X X is a‎ ‎Baire space if and only if X X is Volterra‎. ‎We show that if X X ‎is a metacompact normal sequential T 1 T1 -space and X X has a‎ ‎σ σ -closed discrete dense subset‎, ‎then X X is a Baire space‎ ‎if and only if X X is Volterra‎. ‎If X X is a generalized ordered‎ ‎(GO) space and has a σ σ -closed discrete dense subset‎, ‎then‎ ‎X X is a Baire space if and only if X X is Volterra‎. ‎And also some‎ ‎known results are generalized‎.