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 $G_{δ}$ -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