I know your goal was probably about blocking dust from getting into your display case. But that is probably a lost cause. Dust is fine and it will find it's way in. If there's gaps around the light fixture in the top, or through hinges, you'd be surprised. I think it's just best to attack the dust problem in the room directly.
I have a bedroom with open shelving (on adjustable metal brackets going up the walls) for all my robots (and garfields, I collect vintage garfield crap). It's the cheapest way to get lots of display space. 6 8-foot long shelves 16 inches deep.
Anyway, obviously there's no dust protection! And we have two cats.
In fact before I even put up a single robot I was determined to solve that issue, because I never, ever, EVER wanted to have to dust them!
I ended up deciding to go with an air purifier. It will constantly exchange all the air in the room around 6 times an hour. It also emits negatively charged ions to dislodge dust (note this is NOT the same thing as ionic breeze-type machines which emit ozone, you don't want one of those).
As with everything I buy, I researched for a couple months, looking for the best quality at the best value. (I don't want to sound like an advertisement, but PM me if you want to know my brand/models of choice). I will say though that you absolutely want a unit with a higher up front cost, but the filters only need to be replaced every 3 years. The yearly cost ends up being a fraction of those cheap consumer models that require regularly costly filter replacements. They're the inkjet printers of the air industry.
I also have a real glass display case in the dining room with some rocks and shells. And I was getting tired of dusting that (once a year before the winter solstice party).
So I just recently got another air purifier for the dining room, placed next to the display case.
If you ever look in a sunbeam shining through a room, you can see all the dust particles swirling around. After installing the air purifier, the sunbeam is dust free! And as a bonus, the air smells cleaner and the pet and food odors are gone.
And the results speak for themselves. It's been over 7 years since I setup my robot room, and I've never dusted it, and I occasionally run my finger across the bots and shelves to check and there is still no dust accumulation.
Also, regularly vacuuming with a HEPA vacuum helps. And you want a vacuum that is completely sealed, otherwise it just blows the carpet dust back into the air out cracks and gaskets in the machine. I researched that for a while too (again don't want to sound like an ad, but PM me if you want to know my choice).
