Volterra space

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

Definition

A topological space is said to be a Volterra space if the intersection of any two dense $G_{\delta }$-subsets in it is dense.

Relation with other properties

Stronger properties

• Baire space

There has been a lot of research on conditions under which Volterra = Baire.

Metaproperties

Hereditariness on open subsets

This property of topological spaces is hereditary on open subsets, or is open subspace-closed. In other words, any open subset of a topological space having this property, also has this property

References

• On Volterra Spaces II by David Gauld, Sina Greenwood, and Zbigniew Pitriowski, Papers on General Topology and Applications, Ann. New York Acad. Sci. 806 (1996), 169-173
• On Volterra Spaces III by David Gauld, Sina Greenwood, and Zbigniew Pitriowski, Topology Proceedings, 23 (Spring 1998), 167-182
• Volterra spaces revisited by David Gauld and Jiling Cao, Journal of the Australian Mathematical Society, 79 (2005), 61-76