There are few items that are specialized for a gamemode/map but there are also a few items that are specialized for champions.
Odyn's Veil for example is only available in dominion and
Prototype Hex Core is only available for
Viktor. The items are not showing because they are impossible to purchase at that time.



The system allows you to put items in the set that your character can't buy, so that can cause some confusion. For example,
Rod of Ages has two different versions for summoner's rift and the rest of the maps, so if you put the SR version of RoA on ARAM, you won't see it in your set. Character specific items are more obvious but it's the same deal.
This is also an intended functionality. This way you can do an item set for a bunch of mages and include viktor, but he'll be the only one seeing the hex core upgrades you put there, for example.

This is also an intended functionality. This way you can do an item set for a bunch of mages and include viktor, but he'll be the only one seeing the hex core upgrades you put there, for example.

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Have I missed something? This seems like it would be a pretty important deal to know and if I set an item set to be specific to a character, the item shouldn't even be able to be placed in the item set.