Volterra space explained

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 Volterra space is Baire.

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.