*Definition [#v1d50e9d]
A space X is locally truly weakly pseudocompact at a point x in X if there is a basic system of open neighborhoods N of x whose all of elements are [[truly weakly pseudocompact]]. If X is locally truly weakly pseudocompact at every point, X is simply called locally truly weakly pseudocompact.
*Reference [#p8113e07]
O. Okunev, A. Tamariz-Mascarua, ''Generalized linearly ordered spaces and weak pseudocompactness'', Comment.Math.Univ.Carolin. 38,4 (1997)775–790.