Volterra space

In mathematics, in the field of topology, a topological space is said to be a Volterra space if any finite intersection of dense G_δ subsets is dense. Every Baire space is Volterra, but the converse is not true. In fact, any metrizable space is Volterra.

The name refers to a paper of Vito Volterra in which he uses the fact that (in modern notation) the intersection of two dense G-delta sets in the real numbers is again dense.

References

Cao, Jiling and Gauld, D, "Volterra spaces revisited", J. Aust. Math. Soc. 79 (2005), 61-76.
Cao, Jiling and Junnila, Heikki, "When is a Volterra space Baire?", Topology Appl. 154 (2007), 527-532.
Gauld, D. and Piotrowski, Z., "On Volterra spaces", Far East J. Math. Sci. 1 (1993), 209-214.
Gruenhage, G. and Lutzer, D., "Baire and Volterra spaces", Proc. Amer. Math. Soc. 128 (2000), 3115-3124.
Volterra, V., "Alcune osservasioni sulle funzioni punteggiate discontinue", Giornale di Matematiche 19 (1881), 76-86.

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