  Consider a mobile sensor network, in which each sensor covers a ball. Sensors
do not know their locations, but can detect if the covered balls overlap. An
intruder cannot pass undetected between overlapping sensors. An evasion path
exists if it is possible for an intruder to move in the domain without ever
entering a covered region. We examine two time-varying topological spaces
arising from such mobile sensor networks. These examples were constructed by
Adams and Carlsson to show that the time-varying homotopy type of the covered
region does not determine whether an evasion path exists or not. One of these
spaces has an evasion path and the other does not, which means that the
uncovered regions are not time-varying homotopy equivalent. We show that the
covered regions of these spaces are not time-varying homeomorphic, even though
they are time-varying homotopy equivalent. We then elaborate on this
time-varying homotopy equivalence between the covered regions.
