As a player I want a filter or sort order that has been applied in a room (Training Room, Elite Training Room, etc) to persist until I leave the room or clear the filter, so that I don't have to keep reapplying the filter or sort order continuously.

Example:
In the elite training room, sort by Power Score instead of Level. Select a hero to view their statistics, then press "Back": the list is now sorted by the default (Level) again
In the elite training room, filter on 3* characters only. Select a hero to view their statistics, then press "Back": the list clears the filter and shows all star levels

Any applied filter or sort order should stay in effect for the duration of being in that room, not reset after drilling down into the sorted/filtered list