  This paper introduces proximal path cycles, which lead to the main results in
this paper, namely, extensions of the Mitsuishi-Yamaguchi Good Coverning
Theorem with different forms of Tanaka good cover of an Alexandrov space
equipped with a proximity relation as well as extension of the Jordan curve
theorem. In this work, a {\bf path cycle} is a sequence of maps
$h_1,\dots,h_i,\dots,h_{n-1}\mbox{mod}\ n$ in which $h_i:[0,1]\to X$ and
$h_i(1) = h_{i+1}(0)$ provide the structure of a path-connected cycle that has
no end path. An application of these results is also given for the persistence
of proximal video frame shapes that appear in path cycles.
