*Definition [#l10e7a24]
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 [#z6272368]
-It is not a property for topological spaces, but subspaces.
-See [[pseudocompact]]

*Reference [#j14936e9]
A.V. Arkhangelskii and Khamdi(Hamdi) M.M. Genedi, ''Properties of placement type: Relative strong pseudocompactness'', Proc. Steklov Inst. Math. 1993, Issue 3.