The Zeno effect has been defined and discussed theoretically, and even proved experimentally, only in connection with time-displaced wave functions. This time displacement corresponds to the measurement time of the relevant experiment. If this experiment is repeated successively a very large number of times in a finite time where, in the limit of dense measurement, we take an infinitesimal measurement time, then the initial state is preserved. This is the usual definition of the Zeno effect. In this work the Zeno effect is discussed explicitly in connection with space-displaced wave functions. Here the repetition of the same experiment over the time axis is replaced by simultaneous performances of the same experiment in a number of identical independent nonoverlapping regions of space. We show that when these regions of space shrink infinitesimally (corresponding to the infinitesimal shrinkage of the measurement times in the time Zeno effect), then we obtain a space Zeno effect, that is, the simultaneous performance of such closely spaced experiments has a null effect.