 We demonstrate how the filtration and paths can be applied to a variety of applications in which defining a metric is not obvious but a cover is readily available.
<clarity>  We demonstrate how the filtration and paths can be applied to a variety of applications in which defining a metric is not obvious but a cover is readily available.
 We demonstrate how the filtration and paths can be applied to a variety of applications where a metric is not obvious but a cover is readily available.