I agree with Hick--an open closet door is definately not enough ventilation.
Years ago, when I first started growing indoors, I had a chance to talk to a true master marijuana grower. I asked him "what is the main factor that most indoor gardeners fail to provide?" and he said "ventilation."
I thought "yeah sure". How could ventilation make that much difference?
I went out and spent $1,000.00 for a kick-ass CO2 system. The whole 9 yards--tanks, emitters, regulators, extra timers & fans, a completely sealed growspace, even an atmospheric (CO2) ppm meter (which cost $500.00!).
Then I remembered what the master gardener told me years earlier, and when I added a chamber, for that one I put in kick-ass flo-thro ventilation.
And discovered that all the letter perfect CO2 augmentation provided me with was shaving about 6 days off of the rooted clone to finished bud time.
A thousand smackers, weekly trips lugging those freaking scuba-looking tanks to the welding shop for re-fills just to have my pot 6 days earlier.
6 days quicker turnaround for a large commercial grower is an advantage. CO2 provides phenomenal growth compared to crappy ventilation. Even vs. excellent ventilation the growth rate is impressive.
But I don't think it's worth it for the average home grower.
Also, ventilating with an open door presents a real problem when it's 12/12 time. Are you going to be there EVERY time to open the door when the lights come on and and be there EVERY time to close it when the lights go off 12 hours later? For 2 months in a row?
For most people, excellent ventilation can be accomplished with 2 $13.00 bathroom exhaust fans from homedepot and a half hour with a saber saw & screwdriver.
P.S. strains are different, but with excellent ventilation it takes 3 weeks to take my 3" rooted clones to 15" tall lush bushy beauties.
P.P.S. although it's generally impossible to provide too much ventilation, avoid fans that are named "The Katrina". You'll blow off the back of your house and find alligators in your underwear.