Definition
Let X be a topological space and Y be its subspace. Y is called strongly pseudocompact in X iff every family R of open sets in X and intersecting Y that is locally finite at all points of Y is finite.
Remark
- It is not a property for topological spaces, but subspaces.
- See pseudocompact
Reference
A.V. Arkhangelskii and Khamdi(Hamdi) M.M. Genedi, Properties of placement type: Relative strong pseudocompactness, Proc. Steklov Inst. Math. 1993, Issue 3.